It was always my belief, from when I first played Chrono Cross, that the Frozen Flame was a tool Lavos used to manipulate the creatures on the planet so as to gain their DNA.
At the end of Chrono Trigger you discovered that Lavos' agenda was simply to take in all the DNA from all of the inhabitants of the planet, and that terror was expressed that all creatures had been raised like cattle.
A good reference to this would come from the game Xenogears, and though primarily written by Soraya Saga, Masato Kato wrote parts of it. Chrono Cross was written after Xenogears...I will explain.
In Xenogears the presence of the Zohar on the planet permeated it with an energy presence called Phenomenon Phase Shift. This power, though alien to the planet, was recognized by those living on the planet and they were able to utilize it to build machines. Eventually, though exposure to this power, humans evolved to the point where they could manipulate Ether Powers (Magic). Further still, Phenomenon Phase Shift governs more than simple fuel and magic needs, it can literally alter destiny if a strong enough willpower presents the desire. Therefore, if someone of strong enough Will wants something bad enough, the Zohar will calculate all possible phenomenon eliminating them down to where only the desired phenomenon still exists.
This is a very similar situation as in the Chrono games. Is the term Chrono Trigger (as originally presented in Chrono Cross, written after Xenogears) relevant to this example?
Let us assume that Lavos is from a species that literally exists as a parasite of planets. If Lavos does in fact grow from the absorption of DNA, then simply dwelling within a planet for ages is a poor way to farm it. The Frozen Flame was inserted in the world, likely in the Primeval Era, where it set about "manipulating" the creatures on the planet for its own purposes. The fact that it eradicated the Reptites first would present an intelligence perhaps recognizing better potential for longevity from the humans. Later, in Zeal, society had reached a zenith, but Lavos was not full, so he destroyed Zeal.
I believe that the Frozen Flame exists solely to get Lavos food via the manipulation of time, species, and destiny.
The term "Arbiter of the Flame" can very likely be directly tied to a living creature on the planet that would best serve Lavos' will, such as the Queen of Zeal, and drive the to acts in the service of Lavos. When the Queen, "regained her humanity" she was taken from this service and thusly granted her own will (or she was killed).
Another similarity, which will only serve to grant credibility for my beliefs, is that in Xenogears Solaris uses the Memory Cubes (save points) to gather information about the surface dwelling humans. In Chrono Cross you find out the Memory Pyramids serve and identical purpose to Chronopolis.
I am not saying that CC ripped off Xenogears, I am stating that it is likely that Kato's influence on the plot of Xenogears he again used when putting together CC.
So here is a diagram of my logic:
1. Lavos enters planet, dispatches Frozen Flame.
2. Frozen Flame examines all current factors on the planet and then takes steps to isolate those with the most possibility and nurture them.
3. Lavos is maintained throughout the timeline by the subtle actions of the Frozen Flame.
4. A fully matured Lavos emerges from the depths of the planet, discharges its progeny, and its life-cycle is completed.
Now, in opposition to this, we can state that the -Entity- is some manner of ethereal sentience of the planet itself. To defend itself it determines key places in its own timeline that can be used to disrupt the destiny manipulating actions of the Frozen Flame and then elects to aggregate its will around a single individual (Chrono).
This person could very likely have been engineered by the planet itself. Regardless, it gives this individual the ability to access the timeline in different points in such a way as to first educate, and then empower the individual. The plot points of Chrono Trigger and their convenient order is even noticed in-game by Lucca who develops the theory of the Entity.
Not every single action from the two games would be a literal action taken by one of these two parties, but it is clear that manipulation from one of these two forces is responsible for very many of the greater changes to the planet's history particularly regarding the presented timelines in the game.
In Chrono Cross the mission of Lavos will have changed from Trigger, and of course the mission of the Frozen Flame will have as well, though a very similar logic can be ascribed.
Chrono Trigger = Keeping Lavos alive.
Chrono Cross = Bringing Lavos back to life.
There are of course far more many mechanics to this world such as a changeable timeline and parallel dimensions. The origin of these mechanics cannot be divined from the games themselves, but what is stated are some of the methods by with which to manipulate them. It stands to reason that if a planet is -alive- that it may option use of mechanics such as time/space manipulation.
This does not cover every variable of the plot, but I believe it is a strong basis for what Kato believes. We know that he wrote some parts of Xenogears, and there are a number of similarities between Deus/Omega and Lavos. The literal specifics are different, but the inception and goals are strongly similar.
If you want me to elaborate further, I can, but I think you all can see my position.