Well Zeal was clearly going for agelessness because I'm fairly sure she's dead by the end of CT. Or at least, agelessness is what she got. Not even Lavos or the Entity are immortal in the Undead Pirate Skeleton sense of the word.
Though, to be fair, it does seem that Lavos is immortal in the D&D Troll sort of way (that is, is seems like one can cut a piece off of Lavos, such as the FF, and still have it function).
So, to address the original question (how does Lavos play into immortality), it would seem that this is by specifically counteracting the normal aging process. As Cerestryo noted, this would include "cell regeneration." Or more exactly, it most likely involved affecting the telomeres (which are what influences how many times a cell can replicate before its dead). Presumably this would require a high level of telomerase (the stuff that repairs the telomeres). Cancer cells tend to have high levels of this.
There is a bit of poetic justice in the immortality granted by Lavos being cancerous in nature. The emanations of Lavos may very well stimulate the production of telomerase, thus preserving the cell life and allowing the body to live (in a way) indefinitely. I, admittedly, understand aging only to a limited degree, but to my understanding a child subjected to this effect would still age physically but not cellularly.
There is more to aging than just cells, however. Our skeletal structure starts out very cartilage but ossifies over time. While not particular an impediment to immortality, it is to eternal youth. Excessive bone growth (in the form of spines) is responsible for the hunched appearance of many older individuals; their bones have grown to such a manner as to no longer allow for proper upright posture. As Queen Zeal lacks a hunched appearance in 2300 AD, this process has been subverted somehow. The two simplest solutions, in the Chrono Series at least, of accomplishing this would be to correct the misbehaving bodily functions that results in this and to simply pause the process.
Given that Lavos (and specifically the Lavos spawn) seem to develop and grow, it is unlikely that ceasing all physical changes is possible from Lavos "radiation." Which then leaves the possibility that something about Lavos' energy encourages bodily functions to achieve perfect efficiency. That is, cells replicate perfectly (never having potentially deadly mutations occur), bone deposits are at the perfect level to maintain proper bone density but not to form aberrant growths, new cartilage is produced at a perfect rate to replace tissue damaged in the normal course of life, etc.
The only potential cause of this, as far as I can tell, is in the foodstuffs that Lavos consumes. He is feeding off of the planet and producing energy similar to the planet (there being both natural and Lavos based magic, one would assume the energies involved are at least similar). As the planet's energy seems to be related to vibrant life (and thus when near drained the world looks like it is ruined), so Lavos' energies might likewise be such.
Which is all a very verbose and round about method of getting back to what Faust originally said: "Lavoid Emanations."
It would seem that there is something about Lavos energy, particularly in high doses, that promotes "perfect" cellular and bodily functions. This may be related to the fact that Lavos is like the Borg, searching for biological perfection by absorbing the elements of creatures on the planet it inhabits; bio-components that degrade would be averse to this goal. Standard biological processes could still happen, but aberrant processes (such as those related to the decaying aspect of aging) would be suppressed.
As the Mammon Machine works as a focal point for Lavos' powers, it seems that mere proximity to that (and not Lavos) is more important, especially once a connection had been made to Lavos. I am not sure Lavos awaking was necessary, but the energy extraction (which resulted in Lavos subsequently awakening) was.
Of course, once these functions have been suppressed, they might remain suppressed or, at least, be far easier to maintain (just like it requires less energy to keep a house cool than to cool it down).
