Anime & Donghua

I haven't vetted it yet, but fans of Lain tend to recommend Paranoia Agent and vice versa, and they sound similar enough to each other. But have you already seen Neon Genesis Evangelion? Because that's another one that's got a lot of vice-versa recommendations with Lain, and I've seen it twice now and I would say that it scratched a similar itch for me as Lain did, although Evangelion can at times also be more action-oriented than Lain, what with the mechs and all. (By the way, if you enjoyed Evangelion you should also consider Nadia: The Secret of Blue Water!)

I didn't manage to get into Madoka Magica myself, but maybe that's something for you, if you liked Lain for this teenage girl getting pulled into the web of this sort of dark underworld. I also think Lain has a lot of fan overlap with Revolutionary Girl Utena and FLCL, though I haven't vetted more than the first two episodes of either of those. Utena and FLCL aren't necessarily that similar to Lain in terms of tone or content, but they are late '90s to early '00s "auteur" type stuff, so if the "auteuriality" of Lain was a major draw for you — as it sounds like it was — then Utena and FLCL could also be up your alley.

…But I mean, that's the problem with "like", isn't it? The whole question of "'Like' in what way?" Because I could even recommend Steins;Gate as a top-tier psychological mystery show involving a lot of tap-tapping on a computer keyboard, but the vibes just aren't the same as Lain, 'cause Steins;Gate has a lot more levity, for one.

So yeah. The recommendations will always depend a lot on the specific point of comparison. But I still hope this is a good jumping off point.

SEL was the thing that made me realise that there was anime that wasn't juvenile power fantasies for disaffected boys.

Could also recommend paprika for some mind melting reality blurring stuff.

Ghost in the shell is very good and similarly existential although a lot more straight forward.

edit: different vibe but similarly artistic and distinct are ?shinechiro watenabe?'s animes. Cowboy beebop, samuri champloo stand out. The wife and I adored space dandy for blending ennui, absurdism, and a dandy guy in space but it's defs the most juvenile

Not an anime but you could play the PS1 SEL game

https://www.youtube.com/watch?v=Rm47V1O78Ts

Boogiepop Phantom, the original season is extremely similar. About as good too.

Seconding @WokePalpatine@hexbear.net to say Boogiepop Phantom (the original/first season) is very good and feels very much like SEL!

Haibane Renmei was directed by the one of the key animators of Lain, and shares it's character designer. It's very good, if a bit slow and existential.

Kino's Journey (2003) was also directed by Lain's director, it has a similar surreal feeling but I think I like it a bit better than Lain because it touches on things like politics and identity.

Other posters have already given good recs (I'll vouch for Paranoia Agent and the rest of Satoshi Kon's work), but if you're willing to change the genre to fantasy Mushishi is really good and also contains that same kind of thoughtful mysterious vibes.

The Ghost in the Shell movie, and particularly the sequel, felt close to SEL in their contemplation, while the GitS series explored the larger social aspects at the expense of the SEL vibe.