Let me first say that i'm holding on to these beliefs as loosely as someone possibly can. Mainly for the fact that I think I probably missed or misunderstood something along the way, warping my view of the ending. But whatever.
At first I thought that maybe Lain was playing a Jesus type role, in the sense that she sacrificed herself in the reset to save everyone else. At the point of her creation, Eiri gave her a false family so he would be able to control and use Lain, but with Lain being more powerful she is able to defeat this false God, and then she is able to meet with her 'father' or real God after the reset in that small tea party. But in all honesty I don't like this theory, and i'm not sure why.

A theory I like is that the real world is all a computer simulation and everyone in it is just a program or AI (the main reason I like this theory is it makes the deaths and deleted memories make a little more sense to me). Eiri is the creator of Lain, who is designed to tear down the wall between the real world and the Wired. But like Eiri, Lain is self-aware and starts a journey to enlightenment, and realizes the real world and the Wired are both as real as each other. And later after the reset becomes an omnipotent being who watched over both worlds.

There are a couple more theories I've read that talk about Lain being the combined unconsciousness of the planet. Or Lain being created by alien intelligence (her father being an alien) but I leave them for another time.