It absolutely was repopularised by Lil B, I was there for it. My understanding at the time was that it was a reclamation of the word from an original slang meaning of being strung out on crack. Lil B was celebrated ironically by the 4channers that later propagated the right wing appropriation of the term. I always interpreted that to refer to being strung out on ‘the red pill’ i.e. being unapologetically fascist.
I don’t know anything about the origin of the new use of ‘cap’. No one was saying ‘based’ in proto-internet culture before Lil B’s music videos around 2010-2011. This guy blew up quick and he used the word in his nickname. It was his version of BRRRR for Gucci, FLOCKA, etc. That’s just a fact.