It doesn't comply with the PD principle unfortunately. I forgot to take this principle into account in my middle paragraph in my previous post.
The premise of CT is that Lavos has "already" destroyed the world in 1999 A.D. once, and thus the Entity sends Crono on his quest through time to revert this Apocalypse. But if Lavos has already destroyed the world, this means he already exited his PD, so shouldn't this PD be dissolved for all the timeline? The PD shouldn't be able to appear in 12,000 B.C. after the Black Omen, since it has already been dissolved (or at least it should be empty, with Lavos away). It's like, instead of having a Lavos with no shell, there shouldn't be a Lavos at all... unless the Lavos that appears is the one that emerged in 1999 A.D. (the "present" Lavos).
The "no shell" detail seems to be a proof that it's really the 1,999 A.D. Lavos that appears in 12,000 B.C. If you defeat his shell in 1,999 A.D. and go back to 12,000 B.C., Lavos will appear after the Black Omen with his shell defeated. This means he emerged from his PD in 1999 A.D., may or may not encounter the party depending on their actions, and then he reenters his PD to go all the way back to 12,000 B.C., either summoned by Queen Zeal or on his own will.