Ok, here's the scope.
Gast was a scientist, who studied the Ancients, or, Cetra. Hojo and Lucrecia were his assistants. Vinny was there as protection.
Gast found what he THOUGHT was an acnient at the time: Jenova.
But that wasn't enough for him, oh no. He wanted a living, breathing Cetra.
Knowing that Hojo and Lucrecia were an item, he waited for them to conceive a child. While the child was in utero, professor Gast (with hojo and lucys permission, though vinyn objected) injected Jenova's cells\dna into Lucrecia's womb. That way, the child would be a human/jenova hybrid (but he thought he was making the child a human/cetra hybrid).
The result was Sephiroth. Human in apperance, with the powers of a god-like entity, though these powers were never fully realized until much later in Sephiroth's life.
Anyway, After that, Lucrecai dissapeared. We see in the flashback that she cllapses, casuing vinny to go apeshit. This results in hojo shooting him, mucking him up, and thrwing him into the side room in the basement. Lucrecia evidently fled. Gast, too, left, after freaking out that Jenova wasn't an Ancient (Naaw, ya think?!), and that he may have helped concot a monster (later meeting iflalna).
Lucrecia dreams of Sephiroth because she has J-cells, that which the clones all have, and links them to him. Lucrecia probably has a smaller percentage then most injectes, as she has them in a second-rate sort of way. Vinny tells her that Sephy is dad, becasue it was much easier for him to say that than "Oh, yeah, he's alive. He's planning on destroying the planet and becoming a god becasue he went nuts which is all your fault for allowing the experiment, oh, and by the way, my friends and I here are on a quest to go kill him" =P
