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 "You will have to remain not only until you learn the procedure," Lew was informed, "but until we are sure of you as well. There is a hotel close to here, the Esthonia, which penitents who come to us often make use of. Mention us, they will give you a good discount."

* * * * * * * * * *

This is Drave informing Lew of their offer. "Drave" is an archaic preterit of "drive." Drave is also a noun meaning "a fishing trip in which the members of the crew go as sharesmen, each supplying a net and receiving a share of the profits." The fact that Drave speaks for the entire group with the pronoun "we" suggests that they're some kind of communal group acting as one. So what are they fishing for? And is the "net" which each member brings to the  cooperative project actually their soul?

"you learn the procedure"
Just this short phrase already sounds too involved for me. There's a procedure for atonement? One with rules which you can learn so that anybody can do it easily by simply following these, say, twelve easy steps?

"but until we are sure of you as well"
It's definitely a cult. Satanic maybe? Hopefully!

"penitents who come to us"
A penitent is a person, like Lew, who repents their sins. How do Drave and his group find them? How do penitents find Drave and his group? Something's fishy here. It's like some kind of magical realism horror movie where somebody in trouble wishes for help and suddenly they're in a magic carnival where the barker is all, "Come inside, come inside! We'll make all your dreams come true!" And then there's a sex scene with some boobies and then all hell breaks loose.
    Now you know I grew up watching 80s horror movies.

"they will give you a good discount"
Hopefully that discount is 100% because Lew already told you that he can't pay.

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 "Pay for it!" The tableful of adepts was amused at this. "Pay! Of course you can pay! Everyone can!"

* * * * * * * * * *

Uh oh. This is starting to sound a bit Luciferian! I thought they were going to say, "Aw, shucks! No need to pay! We're here for you buddy!" But instead everybody sitting behind Drave is suddenly chuckling mischievously and exchanging knowing glances while Drave says, "Can't get credit?! No problem!" If Lew has no home, no job, no attachments to anything in this world, how is Drave so confident Lew (as well as anybody who wanders into this liminal space) can pay? Because Lew is going to have to pay with something inherent to his being. Yeah, we all know where this is going! Drave is the fucking devil, isn't he?

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 "Sure, but I can't pay you for it, I don't even have a place to live."

* * * * * * * * * *

In America, every thing of any real value must have a price. Anything else is socialism. Or emulating Jesus. But don't tell that to Christian capitalists because they simply don't want to hear it.

Not only does Lew mean he doesn't have a house or apartment for his living arrangements, he also means he doesn't have a tether to this world. He's adrift with no resources and no way to repay any kindness to him. Isn't it interesting that here in America we automatically think that kindnesses need to somehow be "repaid." It's the whole idea behind "paying it forward." "Paying it forward" used to just be "acting charitably." "Paying it forward" is "acting charitably" with a capitalist twist.

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 "Remorse without an object is a doorway to deliverance."

* * * * * * * * * *

Remorse (or the feeling of guilt) without an object (to the point: the cause of that remorse) is a doorway (or a path, a way, a means) to deliverance (liberation from that remorse and guilt). So Drave is basically saying, "Look! You've got it easy, buddy! You can't remember what you did wrong so you have no idea who you've wronged. Well good news! That makes it even easier to atone for that wrong! Without the object wronged by your actions, the only thing standing in your way of atonement and liberation from the guilt is you!"

Or maybe he's just saying, "The attitude of wanting atonement is the key to a liberated life." Those who seek forgiveness, who want to be better people, even without a concrete pain leading them to this decision, have found the only way to truly be free. Just wanting to be better already makes you slightly better.

Drave is like some kind of other-worldly, back-alley, carnival barker therapist. He is to Lew what blogging on the Internet is to me.

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 "Even if—"

* * * * * * * * * *

This is enough of a statement to extrapolate what Lew is feeling at this moment when Drave suggests they can help him. "Even if they knew what he'd done." "Even if they understood what's happening to him." "Even if they could possibly have a solution to his problem." "Even if" is simply a way to begin a statement which suggests "I don't actually think you can help but thank you for trying."

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 "We can teach you," said one of them, who seemed to be in charge, introducing himself only as Drave.

* * * * * * * * * *

These people are indeed familiar with Lew's situation, waking up in a world one no longer recognizes with no memory of the past people keep reminding you of. So they must also be from another dimension or story or time. Also, the guy's name is Drave. What kind of name is Drave?! He must be from a dimension where everybody has an additional "R" in their name.

Chapter 1: Section 5: Page 39: Lines 76-77 (658-659)

 When their business was done, they invited him over to a table under an awning, where all at once, over root beer and Saratoga chips, Lew found himself confessing "everything," which in fact wasn't much—"What I need is some way to atone for whatever it is I've done. I can't keep on with this life. . . ."

* * * * * * * * * *

This entire scene, with Lew Basnight at the head of it, is reminiscent of a character's definition of magic in The Crying of Lot 49: "another world's intrusion into this one". I'm not suggesting there's something magic going on here! Obviously in this novel, it's going to be something scientific! But it brings up a theme shared by many (if not all? I haven't read them all!) Pynchon novels: one world intruding on another. Here in Against the Day, we get an example of this that's as literal as Pynchon can probably get.
    Already this book purports, in the typical Pynchonian way, to be a "historical fiction" of our own world, thus a world intruding on another world." Then within this world, we have the fictional world of the Chums of Chance novel and the Chums intruding on the Against the Day world from their fictionalized world. And here we have Lew Basnight, almost certainly from a different Chicago on a different world, intruding on this Chicago and subsequently entering another pocket universe of people who seem to also be intruding on this world. What does it all mean?! I don't know. I never got my Master's Degree in Literature.
    Who are these people and what world are they from? It's like Lew has found himself on the set of a PBS kids show, Sesame Street or Villa Alegre. They are just as welcoming to strangers as you'd expect a character from one of these shows. Is it because they, too, have somehow intruded upon this world in their own waking swoon? Is that how somebody winds up living on Sesame Street?

"I need is some way to atone for whatever it is I've done"
There are two major ways to get through life: denial or atonement. Most people choose denial, the most popular form simply being passive distraction. Books, movies, video games, drinking, drugs, sports . . . you name it, it's been done in the name of trying to forget about death. It's a hell of a motivator, really. Sitting around bored too often leads to existential thoughts and morbid fantasies.
    But some people, probably those with the most finely tuned sense of self-reflection, choose atonement. Even if, like Lew, you can't really put your finger on what you need to atone for. There's certainly something because we're social beings who live our entire lives surrounded by other people while we allow our selfish desires and motivations to guide us. There's going to be a lot of collateral damage along the way, seen and unseen. You don't have to have a religious bone in your body to understand that maybe you owe the other people trying to get by in life along with you an occasional apology. That's mostly what atonement is. It's just saying, "I'm sorry," to anybody and everybody and yourself.