Well, as you wish, it is your story after all. I was only hoping to give a little kick in the tailpipe, as you said.
As a suggestion of what the reason for knowledge could be... perhaps a fear of death? A fear of death could have lead him on a search for the secret of immortality, much like Gilgamesh - maybe even a comrade of his of the ancient world fell victim to this immortal power called 'death', and in fear of it he began searching the universe over for the secret of immortality. But unlike Gilgamesh who but finds immortality to be the secret of the gods, and unnattainable, he indeed found it, but in possessing it found it to be a terrible curse, for in time his strength failed in despite of his immortality, and he thus sought no longer for immorality, but for the power he was now lacking. And seeing how despicable his weakness was, he resolved to clothe himself in an aspect of supreme power, to be not only immortal but mighty beyond compare. Thus he sets into motion a plan of millions of years to take the life of worlds and make it his own (I suppose like Sephiroth and the meteor, but much more subtle and long-lasting an attempt.) This could also then account for his long sleep. But in his long life his mind has been scattered - for despite immortality, he is still a mortal in spirit, and his 'dream', as it were (borrowing the terminology from CC) has strayed so far from Zurvan, it has lost order and coherence. Thus he becomes insane, in some regard, even as his grand plan comes to fruition.
So, essentially, first comes a fear of death. From this stems the desire for immortality, knowledge being a pathway to this. To attain this, he makes a Faustian pact, either in some actual way with a mightier creature (the death itself, Thanatos, that he so greatly fears, maybe?*) or simply in a metaphorical way. But after many long years of this wise, intelligent, life, he begins to find that knowledge does not breed satisfaction, and that weakness still sets in - the death he avoided has been replaced by a wasting away. In terror of this he uses his supreme knowledge and dark-learned arts to perfect a plan to become mightier than aught else in the universe, so that he might never have to lack power, or fear for anything. So that he could live forever unassailable and without care. And whiles this occurs, his spirit has ceased being one of order, and has rather turned to chaos. So, that brings us to CT, and his master-plan of turning the earth into an immortal throne where he can live forever. But in all this, he has ceased to be 'human' (or whatever he was to begin with) - all that he was, defined by cares and even death and mortality, is gone, so what now is he? He is unique, a terror and tyrant who looks only to himself. But, in origin, he need not have been any more than a mighty Dr Faustus mingled with Gilgamesh; he may even have been a hero! The Chrono series is an epitaph to the tragedy of Lavos, then, for this wretched creature that wishes so much power and destruction was no more than what man is.
By the way, did you consider the Greek stuff?
*(Note: Read this after all the rest of the things) Yes, that may be it, that may be Mephistopholes and Satan in one in the Chrono world: death and nothingness. In Greek death would be Thanatos. But there are other powers yet older than Thanatos, perhaps throw versions of these together. The ancient four of Greek myth were Gaia - likely the entity in CT -, Chaos, Tartaros, and Eros, of which Chaos came first. In Chrono we already have Gaia taken care of. But what of Chaos, the eldest? What of Eros, that is Desire? Tartaros the Pit? The great creature Typheos the Terrible is born of the union of Gaia and Tartaros, maybe that give some story ideas for some boss, just as a side-thought. Alright, just bear with me here, the ideas are a little scattered in my mind, and my only hope is that you take them and somehow find some value or coherence in them that might be of use. These are basically how the Chrono world connects with Greek mythology; it might be something to continue on, to some extent. Now, as I was saying... Kronos the youngest of the Titans, at the bidding of his mother Gaia, took up an adamantine sickle and castrated Ouranos, allowing for the imprisioned hundred-handed, and various other creatures, to come out of Gaia. It also usurped Ouranos' position as supreme god. However, Kronos was surplanted by his own son Zeus. Now, take this connection: The planet as Gaia (plainly), Crono as Kronos, and Lavos as Ouranos (for Lavos did come from the heavens, and caused great pain to the earth, did he not?) What does the the Planet do? She takes a son of hers, one of the youngest (being born in a late age - remember, too, that Kronos is a son by Gaia and Ouranos... is not mankind in CC the progeny of the Earth corrupted by Lavos?) and giving him power sends him to render her vile opressor impotent. He succeeds, even as humanity succeeds in freeing earth from Lavos. But guess what! Kronos was an even worse tyrant than Ouranos, and Gaia conspires to rid herself of this new menace: mankind, her aforetimes saviour. Very much alike, eh? Now, obviously the rest of the tale, like the Time Devourer, and the like, don't connect exactly... but they don't have to. This is enough to cement a very typological similarity. What you can have thus is the history of Lavos/Ouranos before this, not the exact same, but borrowing ideas. Thus Gaia is older than Lavos, and Lavos itself is born of Gaia (or, at least, one of the 'Gaia's' of the universe.) This accounts, so far, for only one of the four original beings. Eros... connects everything, and needn't be directly addressed. Tartaros and Chaos, though. I cannot remember how they connect to Thanatos...
First, an interjection. This does not contradict with my Faustian idea with Lavos. That was a concrete story idea, of Lavos originating as a being on another planet. This is more of a mythical view of it, seeing Gaia as far older, and Lavos coming in the mists of prehistory as an oppressor, and Crono/mankind as a saviour at first, and later oppressor. Both still hold uncontrary. But now that the connection between my Faustian Lavos and the Ouranian Lavos is cleared up, I can connect him with what can be maybe the older and more powerful things that he fears as a Dr Faustus. It must be noted with extreme admonishion that these older powers should not be considered evil, or uber-bosses or uber-evils to outdo Lavos. He fears them, but they are simply the things of the Chrono universe, and not the enemy thereof. Thus Lavos, though he makes a pact with these things, is still the chief of evils. Just like one in old myth might make a pact with Hades, and become embittered through it, Hades remain not evil: he is pityless, but cannot be held to be evil. He just is what he is. Now, as I was saying...
I have to look at the Theogony for this. Alright, from Chaos comes Erebos (the Darkness) and Night. From Night comes Death (ie. Thanatos in Greek), Doom, and Fate. Now, I'm not sure how this all can go together, I admit. Basically, I would say, do only passing references to these other entities. Say that Lavos drew his power from hateful Night, being affrighted at the aspect of Thanatos, who had torn from him a dear friend. Or, even, make him go higher up: to Chaos. Tartaros doesn't need to be mentioned at all. But essentially, you can hint at the history to Lavos even as I've already outlined in the rest. But add that at the death of his ancient companion, he becomes terrified of Thanatos coming for him and tearing his life from him. So he begs that he might be spared his visit, and at long last discovers a way in which this might be done - his search for knowledge. At this an enraged Thanatos comes to him, crying that none may avoid him, and that when the hour that his brother Fate decides comes, then he will take his life from him. But Lavos cries to Thanatos' mother Night, imploring her to stay her son's hand, and then up to her father Chaos, who was before all else. And here comes the Mephistopholean bargain, though not Chaos, nor Night, nor Thanatos himself are actually evil the way Mephistopholes and Satan are. They grant that he, because of his great learning, first amongst mortal, need not fall to the hand of Thanatos, and Death consents - but it is a gift of Midas, a curse within a blessing, and they know it. For even as Tithonus the Trojan prince who gained immortality but not eternal youth, he begins wasting away, and forsees an eternity of impotence - more frightening even than death. So he looks now for power, and again cries to Chaos. He offers to give his soul to them, and not to Zurvan (Tartaros?), if they will grant him knowledge by which he can make himself powerful amongst immortals. They thus do, and thus he knows how to do those things that he later does. Certainly, though, Gaia must not be happy, but I daresay she could not do much against Chaos' displeasure. I stress again that these are impartial entities, not evil. It fits better that way.
Anyway, just some ideas. I hope they're useful. I obviously delved much into Greek myth.
So... thoughts? I hope someone at least read through all of that. It took me a while to formulate.