Well, who is it that says that he's a monster from an unknown origin? It's either Miguel or Lucca, I think. He's also called 'the infamous immortal', which seems to imply that his race is naturally deathless. But beyond that... hmmm... well, doesn't Lucca say that it's a cycle: a parasite who's young go forth and do the same to other planets? One must remember, in the Crono world planets themselves have life. Therefore, even as there are diseases of the creatures of a planet, there are those that are foes of the planets themselves, abominations that - unlike the native creatures - do not live in a symbiotic but rather a parasitic relationship. It's just a translation of the micro into the macro.
Now, that was mostly Trigger. Cross makes him more complex. He's no mere parasite. In Trigger he wore armour, hinting at intelligence. Cross takes it further, in that he almost definitely has a will, and his destructive and malefic essence is contained in the Flame, a sort of One Ring of Sauron for Lavos. A wish granter that merely turns things into the will of its true master. Humanity, touched by him, is said to be tainted from natural symbiosis into a form of parasite themselves - a corruption of an original intent, half-way between native creature and Lavos. As if, due to the prescence of a parasite, a cell of the body were to mutate into a new thing, not wholly of either. Lavos, thus, while still being a parasite, is undeniably evil - there is no mere bestial ignorance here. He has a will to destroy and cause pain - an embodiment of that - and lives to cause suffering.
I think the most telling aspect of his nature is on the steps of Terra Tower. Those are the words of the Flame, which has been said to be 'the essence of that which fell from the skies in ancient times.' Thus, the Flame and Lavos are, without any room for doubt, one in the same, of same spirit and will. What the Flame does, what it wishes, may be taken to be that of Lavos as well. Now, the words of the Flame don't give much to go on but, from the impression I get... something else caused Lavos. Something hurt him, badly. Made him angry. Twisted him, and corrupted him, and turned him into a parasite. Something, I think, destroyed his world, and disillusioned the mighty power of his race. Notice, he asks if it's neccessary to destroy another planet in order to survive. He's contemplating the nature of destruction as it's neccessary for life: an animal would not think thus. He has an understanding of his actions. He may even have remorse. But he's holding his own life, his own existance, as most important - he needs the life of another planet to feed his own and continue - BUT he doesn't seem happy with it. He appears to lament that that is the nature of the universe, that he must destroy another so that his life may continue (this is a continuing theme in Cross, I must add - it can be applied to how humanity as well, and Lavos is used as a sort of example of what could be, and from which lessons may be learned.) Also, he says something to the effect that those who feel pain, pass it on to others. Those sound like the words of someone who's been tormented and so twisted by it that he feels the only respite is to inflict it on others - misery loves company, after all. So, here we have a creature who's life - both physical and emotional - depends on suffering and pain. And, if all his race are like this (keep in mind that Lucca in Trigger could have been wrong about his race, in some measure), they collectively suffered some catastrophe that made them all into jaded, universe travelling, psychopaths (literally, in fact, for they feel a deep emotion of the spirit, which is what psychopath means.)
I didn't really approach that in a very orderly fashion, and it would help if I had the trascript of his words there before me. But truly, remember that part, for THAT tells who Lavos is. Sure, you can get a bit of his origin, his nature, from the way he acts. But he's mostly an impersonal monster who corrupts and destroys in Trigger... a foe who never speaks, save through the queen of Zeal. But Cross... the Flame is his voice, and there it is that he speaks. Also, as some have said, there is much that might be learned from what is echoed when people gaze at it. It shows how he twists people, like a distorted mirror. And, by view of the distortion, the nature can be shown. Like I said, if one wishes to know who Lavos is, those two minutes atop Terra Tower are more explanatory than all the rest put together, as it is one of the few times where Lavos actually talks.