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 Not exactly invisibility. Excursion.

* * * * * * * * * *

So he doesn't go invisible. He takes a short trip. One definition of "excursion" is "a deviation from a regular pattern, path, or level of operation." In other words, Lew is leaving his furrow which, as we learned, was the etymology of the word "delirium." He is delirious and it is his delirium that allows him to become "invisible."

I'd also like to point out that sometimes an excursion can become a long-term or permanent change of location. I experienced it myself when I left my hometown to go cross country in my VW bus, winding up leaving California to live in Lincoln, Nebraska, for two years. Meaning, of course, that Lew could have arrived in this Chicago by accidentally performing an excursion that became permanent.

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 Wherever it was he stepped to had its own vast, incomprehensible history, its perils and ecstasies, its potential for unannounced romance and early funerals, but when he was there, it was apparently not as easy for anyone in "Chicago" to be that certain of his whereabouts.

* * * * * * * * * *

Lew is describing another timeline. Probably, by the suggestions of things that could be happening there, a different one each time. Perhaps he even steps into other novels, exiting this one for a slight amount of time while still being able to observe what was happening. So he keeps a connection to Against the Day (or, at least, the Chicago of Against the Day). One can see how he arrived in Against the Day by this method as well. He stepped to the side of wherever he was, entered Against the Day, and then lost the connection with his original world. Perhaps in that moment, he lost both his original past and the past he should have known that was built for him here in this novel. Or, as I've speculated, he simply came over from another Chicago, lost the tether in the same way, and became stuck here.

"it was apparently not as easy for anyone in "Chicago" to be that certain of his whereabouts"
It's as if he still exists as a known character in the book but, for a few moments or so, he is outside the boundaries of the novel, and thus unfindable by other characters in the book. But still observing. Hmm, I guess I said all this in the previous paragraph! I'm pretty sure I've explained myself fully already!

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 He had learned to step to the side of the day.

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Look, I was just kidding about him stepping into some other dimension. In my heart, I knew that was a possibility because this is a Pynchon novel. But my head, which absolutely rules my heart, kicked my heart in the teeth and yelled, "No! That is dumb, heart! Go to Hell!"

So Lew does have a magic power and it absolutely has enough similarity to him crossing over from another timeline to this one to be seen as evidence to the theory of Lew's past life being that of a different Lew from this dimension, and Lew a strange traveler from another having replaced him. He had simply stepped too far to the side of the day one time and wound up here, perhaps filling the vacuum of the sinful version of himself who purposefully stepped too far to the side of the day to leave his sinful past behind him.

"learned to step to the side of the day"
This is perfect phrasing for keeping this seemingly magical ability in the realm of science. First, Lew had learned the technique. And while, sure, you can learn magic, one's first reaction to the verb "to learn" is educational and scientific. Secondly, "stepping to the side of the day" sounds technical. He is performing a feat that can be summed up in simple words, although it could definitely use some clarifying. And we are invoking "day" which syncs up with the title and the theme of light. It also suggests "invisibility," as if he's avoiding light somehow, and thus becoming unseeable by those around him.

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 Lew enjoyed wandering around, trying on different rigs, like every day was Hallowe'en, but he understood after a while that he didn't have to.

* * * * * * * * * *

Poor Lew! He loved to play dress up but ultimately found there was no need. Because he could hide among the sighted as surely as if he weren't there. Could he make the light around him shift? Could he side-step into another dimension, perhaps the one from which he came, the one in which he hadn't sinned so profusely that it ruined his life? Or was he just such a plain looking jerk that nobody gave him a second thought?

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 At White City Investigations, invisibility was a sacred condition, whole darn floors of office buildings being given over to its art and science—resources for disguise that outdid any theatrical dressing room west of the Hudson, rows of commodes and mirrors extending into the distant shadows, acres of costumes, forests of hatracks bearing an entire Museum of Hat History, countless cabinets stuffed full of wigs, false beards, putty, powder, kohl and rouge, dyes for skin and hair, adjustable gaslight at each mirror that could be taken from a lawn party at a millionaire's cottage in Newport to a badlands saloon at midnight with just a tweak to a valve or two.

* * * * * * * * * *

Okay, okay! I get it, Pynchon! I understand what you meant by "a keen sympathy for the invisible" now! This follow-up sentence explaining the "invisibility" line just goes on and on, as if Pynchon knew I personally was going to be confused by what he meant by "a keen sympathy for the invisible" and would have to wade deep into the minutia of clarification.
    "A keen sympathy for the invisible" just means Lew Basnight could really blend in to a crowd. He could eavesdrop anywhere unnoticed. He was a master of disguise and demeanor.

Pynchon loves long paragraphs like this that list lots and lots of things for the reader to visualize. Usually he throws in a bunch of things that the reader probably needs to look up. But not this time! It's all pretty standard costumes, props, and make-up.

I don't know if Pynchon is referencing any specific "millionaire's cottage" in Newport that a detective agency might have cause to investigate (in general, of course, the reference is just because it's where the richest tycoons had vacation homes and the rich are always good for a scandal or two) but I'm pretty sure the "badlands saloon" is Nuttal & Mann's Saloon in Deadwood where Wild Bill Hickok was murdered. Or maybe, again, just a general reference to a place that was likely to host an unguessable number of scandalous incidents.

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 His office and field skills weren't the worst in the shop, but he knew that what distinguished him was a keen sympathy for the invisible.

* * * * * * * * * *

Lew was a mediocre detective who had an ability to see that which others could not. More importantly, with the use of the word "sympathy," he probably had some empathetic bond with the people of Chicago whom the rich and powerful would rather not notice. This is absolutely speculation on my part and probably a healthy dose of projection. But I feel like we're learning Lew was not what Nate Privett actually wanted in an employee. Sympathizing with the less fortunate will cost Nate money since, it seems, Nate's main business is harassing them for the rich and powerful.

Why am I not treating this sentence as literally as possible?! It's a Pynchon novel! He might actually mean that Lew can see invisible things! He already seems to be a dimension-hopping traveler of space and time! Why couldn't he also see invisible things? Remember, this book (or chapter, at least?) seems to have something to do with light! And light has everything to do with making things visible. So perhaps we're going to encounter some invisible beings later, maybe the ones whom Penelope Black and the Bindlestiffs of the Blue encountered over Mount Etna!

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 By the time he got that pleasantry all decoded, Lew found he was more than able to shrug it off.

* * * * * * * * * *

So Lew had to decode that shit too? That's good to hear. Hopefully he came to the same conclusion I did or else I'm off to a really bad start in trying to figure out this book. I suppose as long as I'm consistent in my artistic interpretation of the novel, it's valid! It might not be correct! But my critique still probably has something valid to say about the work.
    At least some of my critique does. Ninety percent of my critique is just plain stupidity and stories about some occasion when I was tripping on mushrooms.

"more than able to shrug it off"
This phrase leads me to believe that I was more or less correct that the statement was office place propaganda to inculcate in Lew a sense that Chicago was becoming increasing lawless and dangerous to the average person. And by the time Lew figured that's what they were trying to do, he was pretty much immune to it. That probably means he'd seen enough on his own, during investigations, to know it was bullshit. Which continues to match my Facebook analogy from the previous entry. If only our conservative friends and family could get outside their propaganda bubble, and actually venture forth into these communities that represent to them lawless anarchy, they'd experience for themselves how untruthful all of those Facebook posts truly are.

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 Next thing he knew, he was on the payroll, noticing how every time he entered a room somebody was sure to remark, ostensibly to somebody else, "Gravy, a man could get killed out there!"

* * * * * * * * * *

I'm guessing "Gravy" was an exclamation around the time and not the name of every ostensible somebody else in the room. Aside from that Nobel Laureate brain sized realization, I'm at a loss for what this means. Does Lew mean every time he walked into a room at White City Investigations, somebody said that? Or does he mean everywhere he went now, people recognized him as an investigator and, for some odd reason, made this exclamation?

Is it possible the people around him are trying to paint Chicago as more dangerous than it is, the way Fox News propagandizes Portland and Chicago and Baltimore and—welcome to the club, I guess?—Minneapolis? So now that he's a part of White City Investigations, Nate Privett wants to make sure Lew absolutely believes what they're doing is making the city safe? "A man can get killed out there with all those anarchist slash labor unionists running around bombing everything!" is the sentiment Lew's supposed to hear, just like all of our terrible relatives constantly hearing those messages on Facebook.

That actually feels right. Lew is now experiencing what our friends and family in right-wing bubbles experience on Facebook constantly. People on every message board constantly saying, "Gravy, a man could get killed out there!"

"Gravy"
Gravy is the name of my cat:

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 Lew nodded and took him up on it.

* * * * * * * * * *

Sure, why not? The man pointed out this job wasn't as morally objectionable as a job with the Pinkertons. Unless what Nate was really saying was that a job with White City Investigations was just as morally objectionable but just didn't pay as much. Remembering how Nate ate his pancakes in a capitalistic fervor, I'm going go with the latter interpretation.

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 "You think working for the Eye's a life of moral squalor, you ought to have a look at our shop."

* * * * * * * * * *

I don't know if Nate meant for this line to be ambiguous or not. I first read it as, "You think you'd be lowering yourself working for the Pinkertons, well, just imagine how much you'll have to lower yourself working for White City Investigations!" I'm sure he means it as "We're more morally upstanding than those jerks so maybe come work for us." But I'm sure Pynchon meant it as, "This guy is telling the truth accidentally. Working for White City Investigations really isn't going to be any different than working for the Pinkertons."

Also, "working for the Eye" has some real Illuminati vibes going on. So that's not as good as a boner joke but a good enough They/Them paranoia reference (unless the Eye is a one-eyed trouser snake joke which I suspect it isn't but if it is, well, then, kudos? I guess?).