Nowhere in the show did it say he was from "Dino Times," also, being an incarnation of the comet doesn't mean he wasn't created by the bomb, Finn is an incarnation of the comet, he was still birthed by Minerva and [His Dad whose name escapes me and I am too lazy to search for].
The Lich could not BE the comet because the comet is a fucking sentient rock. The Lich is an incarnation of the comet. This means, even if the incarnation of the comet that had the soul(?) of the Lich was during "dino times" the point at which the Lich was reincarnated would be the point of the explosion. Much like the point Finn was reincarnated was the time of his birth (not technically, it's implied there were several reincarnations in between but you get the point). In fact, it's not even stated that the comet was the original incarnation of the Lich.
The original pitch for the Lich is much more interesting honestly. It's simple and easy.