Lucrecea--What's with that girl
I always like it when something in a game is only possible to figure out when you think about it a bit. Lucrecea's story is a good example, so here is what I have pieced together. You can completely ignore this post, I'm going to be explaining what I have deduced about Vincent and Lucrecea's origins as well as answering my idea about the question at hand. I'll try to keep it short, so don't blame me if I downplay some major scenes

Lucrecea was working with Hojo in Nibelheim. Vincent, as a turk was sent there also to keep an eye on Hojo. Vincent and Hojo both loved Lucrecea. Vincent proposed to Lucrecea, but she refused because she was in love with Hojo. When Lucrecea became pregnant with Hojo's child, Hojo saw it as an opertunity to see what effect Jenova cells would have upon an unborn baby. Vincent tried to convince her not to do it, but she refused. Her love was so great for Hojo she was going to be his human experiment. Well the plan was a success and a failure. The baby was born, and named Sephiroth (and we all know how that kid turned out), but Lucrecea supposedly died during childbirth (I think they said that part) . Vincent was very very angry and tried to attack Hojo, but Hojo simply saw this as another opertunity to have an experiment and injected Vincent with Jenova Cells.

This is where I get to the question at hand. I'll point out a few facts:

1) Vincent, Sephiroth, and Lucrecea were all injected with Jenova cells (we'll ignore the other people for now)

2) Vincent, Sephiroth and Lucrecea do not seem to age at all from the flashbacks we see to the present day

3) Vincent and Sephiroth are basicly "rock 'ard" and almost invincible. (for Vincent i'm mainly referring to the whole sleeping in a coffin deal)

4) When we see Lucrecea, it is made clear that she wishes to "leave this world" but can't

Phew, so it is my opinion that Lucrecea is alive and could not age nor take her own life because the Jenova cells in her body were keeping her alive. She clearly wishes to die however. When Vincent does go to see her he tells her that her son is dead. The reason for this is usually assumed to be because Vincent wishes to spare her feelings (rather than telling her that her son had gone insane and was trying to kill everyone.) Upon hearing this, Lucrecea disappears. I think that Lucrecea was sort of, like, keeping herself alive just to find out what happened to her child. Once she found out, she could finally rest in piece.

What a long post to say so very little
--Cal