Let's go straight to the problem.
Zaperking pointed out that Lavos was most probably not defeated in 1,999 AD but in 12,000 BC, because of these infos from Chrono Cross which imply that Lavos simply never appeared in 1,999 AD in the Keystone timelines:
[Computer]
~
~
~~~~ -- LAVOS -- ~~~~
~
~~~~~~~~~~~~~~~
An extraterrestrial life-form
that is thought to have
fallen from the heavens
65 million years ago.
On the time line that existed
before history was changed,
Lavos was assumed to have
slept deep below the planet's
surface...
Sleeping and consuming the
planet's energy up until the
day of destruction known as
the '"Apocalypse."'
There are those who believe
that, 12 thousand years ago,
the legendary ancient magical
civilization known as Zeal
came into contact with Lavos.
That fateful encounter is
said to have resulted in
Zeal disappearing from the
surface of the planet within
the space of a single night.
However, the very existence
of the ancient civilization
of Zeal has never been proven,
so up till this day this
theory cannot be confirmed.
On some time lines, Lavos
appeared on the surface of
the planet in the year 1999
and brought the world to
ruins.
However, a group of young
time travelers saw where
their planet's history was
heading and, through their
actions, rewrote time.
This very research facility
exists on that new time line...
In a world where, thanks to
the defeat of Lavos by the
young adventurers, the
Apocalypse never happened...
On a temporal vector where
human civilization continued
to evolve unhampered.
All the data on Lavos that was
obtained from tracing different
parallel world possibilities
has proven to be volatile, with
fluctuating discrepencies.
Perhaps, at this point in time,
it is nearly impossible to
obtain any true information
about Lavos.
Moreover, while it was possible in Chrono Trigger to defeat Lavos either in 1,999 AD or in 12,000 BC after the Black Omen, storyline-wise it makes more sense for Lavos to be defeated in 12,000 BC, because the player is taken straight to his first form after having beat the Black Omen. It's impossible to clear the Black Omen without having to defeat this first form. After that the player can use the Time Gate in Lavos' body to return to the End of Time, but it makes no sense storyline-wise since the party would be much more inclined to finish what they've just started, i.e. to defeat Lavos entirely, rather than to "run away" and leave Lavos' shell there to either regenerate or just be there for 13,999 more years.
However, a problem appears when the Armageddon-Branch Theory is considered. This is a theory which explains why the future was destroyed in Home World:
Armageddon-Branch Theory
GrayLensman
Crono could not have defeated Lavos in Home World. The event which spares Serge's life also creates a plurality of dimensions from 1010 onwards. Since there is only one Crono in 1000 AD to defeat Lavos, only the future in Another World is saved.
Further Explanation
In the original timeline (Another World) Serge dies in 1010 AD, but Kid changes the past, somehow creating an alternate dimension in which Serge lives (Home World). Another World always existed; it is the original dimension, but Home World only extends from 1010 AD onwards. In 1000 AD, Crono exists in Another World. If he travels through time, he can only reach a destination within his own dimension. When Crono defeats Lavos in 1999 AD, or any other time, the battle takes place in Another World. In 1000 AD, there is only one version of Crono. If Crono lived past 1010 AD, there would be a version for each dimension, but that version did not travel through time to defeat Lavos. In Home World, no savior appears in 1999 AD to save the future. Serge caused the destruction of the world by spawning an alternate dimension which is beyond 1000 AD Crono's notice or reach. He does not undo any of Crono's actions. In Another World, the future is secure, at least until the Time Devourer arrives. There cannot be multiple Crono groups because there is only one dimension in 1000 AD!
As you can see, the theory assumes that Lavos was defeated in 1,999 AD. If we assume that Lavos was defeated in 12,000 BC, the theory doesn't work because there's only one 12,000 BC. Lavos would be dead in both Another and Home dimensions.
So, how do we solve this?
