Is this ever explained in a non-handwave manner?
The only explanation I can provide, is by using a real world example - Latin. Like "Caveman-ese" Latin is a dead language, but that doesn't mean it isn't still studied. Additionally, stories from ancient times might also hang around, but only as myth and legend. It's possible that this is what happened with Lavos.
[...] even Lucca, the smartest person in the party, didn't know the word until watching the recording.
Lucca is incredibly smart, but that doesn't mean she can't be ignorant of certain information. (I mean, you might have trouble getting a robotics engineer to come up with anything scientific about the dinosaurs).
As for the recording itself, the file is titled "Visual Recording of the Day of Lavos". At this point, it's clear that the possibility of my "theory" can be a little more concrete. The legend of the meteor; labelled "Lavos" in Caveman-ese, does actually exist, and was not, in fact, a dormant chunk of rock after all. The scientists of the time label it as such, and the whole thing comes full circle.
While the team are more directly involved with the events, and yes, only certain people are present for the "naming" of Lavos, when it first crashes to earth, it doesn't mean that Cavemen don't talk. And I'm pretty sure that a lot of people would have noticed the impact, if only indirectly.
Other than that, there is not much else to explain the link.
EDIT: After going back and playing the game, it is demonstrated that then name "Lavos" is carried throughout the timeline, most likely by the Gurus of the Antiquity Era (12,000 BC). They develop the Mammon Machine to siphon power from Lavos. When you rescue Melchior from the Mountain of Woe, he informs you that
"Lavos sleeps deep underground, consuming the energy" of the planet and that if the Mammon Machine is brought any closer to him, he could awake.
So, at the very least the name "Lavos" has carried up to this point (which could be explained by my previous point). Then, when the Mammon Machine is activated, this creates the time rifts that Chrono and the party use to travel through time - Janus is sent to the Middle Ages, Melchior is sent to the "Modern Era" (1000 AD), Gaspar is sent to the End of Time, and Balthazar is sent to the "Future", or 2300 AD. So, in-game, that means that there is someone that knows the name "Lavos" in each time period.
- Ayla names Lavos in 65,000,000 BC
- The Gurus refer to Lavos in 12,000 BC
- Janus (aka Magus) knows of Lavos in 600 AD
- Melchior knows of Lavos in 1000 AD
- Balthazar knows of Lavos in 2300 AD
- Gaspar knows of Lavos at the End Of Time
This is fairly "hand-wavey", to simply place one person in each time period with knowledge of the creature, but it demonstrates a "knowledge" that spans "all time".