In one of my earlier Thresh games, I would set up ganks with W for my allies, however if the lantern landed on a soul, itd absorb the soul and add a stack. Is this intentional? Or is it only supposed to be his character himself allowed to pick up souls?

I believe this is intentional, but I could be wrong. CertainlyT?

I mean, I understand if it does, seeing as he stores them in his lantern. However the passive states he needs to walk near the souls to take them in.

It's intentional.

the fact the lantern has its own animation for taking said soul?

It's a secret passive, much like the Law of Balance with the ninjas, or the showdown with Kha'Zix and Rengar, or any number of the other little secrets they throw into the game. Thresh collects souls with his lantern - ergo, should his lantern be sitting out there where souls are falling, the lantern collects the soul(s).