Lavos (Binding of)
Survival of villains is a common trope in fiction. It's possible that Lavos faked his death, or used his temporal abilities to disappear to the Darkness Beyond Time (where the party could not follow, possibly) in a desperate bid for survival.
This answer was deprecated by the loss of the Pocket Dimension theory.
Many have often wondered how Lavos was able to bind with Schala, considering he was outright defeated at the end of Chrono Trigger. Some posed the idea of a Lavos spawn being the perpetrator rather than Lavos itself, but this is not supported in the script. The answer lies within the nature of the Darkness Beyond Time. We already know that due to a horrible distortion in the Ocean Palace, Schala was shunted to the Darkness Beyond Time as a physical object (not rewritten history) and left there. Now, considering the Pocket Dimension theory, there existed a future within the Pocket Dimension of Lavos in which he had already destroyed the world and proceeded to spawn. When Crono and the group defeated Lavos directly at 1999 A.D. and later inside the Pocket Dimension, it nullified this future, sending it to the Darkness Beyond Time. The explanation goes, Lavos was able to use Schala, a physical object in the DBT, to somehow prevent its nullification and achieve a physical existence there. The anomalistic nature of the binding and the unique vantage from the Darkness Beyond Time afforded it the capacity to become a Time Devourer.
This primarily relies on established theories regarding time not directly stated in the games, but one more facet reinforces this theory. If you are not familiar with the supposed lost, overarching storyline of Chrono Cross, please read Chrono_Cross_(Lost_Storyline_of). This scenario would reinforce Lavos's ability to interact with Schala. If she were an Arbiter, Lavos would have a direct link with her, and could presumably bind with her shortly after being defeated or as a backup plan.
As for maintaining a corporeal existence, Chronopolis researchers state that the Frozen Flame can manipulate anti-annihilation energy. Some propose that this means anti-temporal annihilation, meaning Lavos can exist there without being negated like the other timelines condemned to the Darkness Beyond Time.
From: Common Questions