I'm looking for a decent kydex AIWB holster for my LCP to replace my current leather holster.  Something fairly minimalist with a 1.5 belt clip.  Most of my go-to holster manufactures don't seem to make LCP holsters.  The Vedder LightTuck seems to fit the bill, but I'm wondering what else is out there.

I'd go with the Vedder if you want a tuckable clip.

I got mine for my LCP II from Bradford Tactical Holsters. Took about two weeks.

I just ordered one for my LCP II from https://wingmanholsters.com.

Should be here Friday or Saturday.

I got a WeThePeople holster for my LCP II.

I'm a overly fat boy and don't AIWB but I've seen a lot of people recommend the LightTuck for AIWB.  I do have one for my Sig P290RS and one for my Sig P250C; both of which I carry around 3:00 and can't recommend them enough for their numerous good traits.  They're also not stupidly priced and have a short lead time and good shipping time.

Caveat - I wear a BigFoot 14oz steel lined gunbelt and need to order the LightTuck's with their 1-3/4" clips for them to work on my gunbelt.  The clips are tightly sized.

crazy as it sounds, for small guns I really like the cheap soft uncle mikes iwb holsters for aiwb. Very comfortable, easy to draw, great at keeping sweat off the gun. I have lots of great custom holsters for larget guns and a few for smaller guns, but often still use the cheap iwb for the smaller stuff.

Carrying AIWB with a holster that doesn't have a reinforced mouth for re-holstering seems like the begins of a how I shot my dick off thread.

I just use common sense and don't reholster until I can do it carefully. If I need to get it out of my hand quickly I'd throw it in an empty pocket.

I hear this a lot "have to be able to reholster it!" BS. You have all the time in the world to reholster. If you are reholstering, the threat is over. Take your time.
It's all these idiotic "yank, fire, ram into holster" videos, trying to mimic a western quick draw, that are utter nonsense.
I like Kydex holsters, and that's all I use. But I'd never tell someone NOT to use a soft shell holster for the reason of reholstering (for the above mentioned reasons).
It's quite easy (and even something people often do with AIWB hard holsters). The answer is... wait for it... TAKE THE HOLSTER OFF. Yep, you take the holster off, reholster, and put the holster back. BAM! Solved. No dick shot, no femoral artery bleed out, nothing.

I blame all these super duper tactical overacting videos for people thinking reholstering is a "thing". It's not. You draw, end the threat, then take all the time you need/want to reholster it.

You'd have to be poll vaulting while reholstering to accidentally pull the trigger on a LCP.

Which is why I don't like the LCP II. I love my LCP (first gen) BECAUSE of it's "safe" long pull trigger. I'll never understand why people want a normal short travel trigger (like the LCP II) on a pocket gun. It's crazy.
I almost feel that way about my P365. It's controls are all "full size" feeling (light short trigger, full size slide release, etc), but it's in a fumbling small package. Fortunately, it's not quite as small as an LCP. People need to keep in mind that super small pistols exaggerate any mishandling.