The theme shown in this project is a classic for those who have read greek tragedies: Is fate predetermined and per se unavoidable or can you overturn fate with free will?
Spoiler They said Lily made an actual choice, "the original sin"... But I think that's wrong. They managed to complete DEUS based on the multiverse theory, so the future/past sims were always the closest version of what (would have) happened. In my opinion they couldn't see their own world, but one that varied by as little as a single choice. They saw Lily shoot a gun in it, while in theirs she'd always throw it away. Perhaps a few worlds further, they don't even die there.
Spoiler You are right, all simulations are alternatives to their universe, however the outcome was never in Lily's hands but Stewart's. Spoiler Though, the "original sin" aka disobedience theory isn't accurate. Think about it, if the machine is God, then it only has power over the simulation world and not their "real" world, because its outside of its predictions, so there isn't any disobedience possible as there was no predetermined path in the first place; they (in theory) were free. Its the intant they die and others input their information inside that they became part of the machine and its rules. They land in Eden (a world without their tragedies) and Forest becomes Adam while Lily becomes Lilith not Eve because in Jewish folklore, God creates at the same time Adam and Lilith from the same clay at his image and likeness.