No she's dead.Lucrecia's full story explained in FFVII Dirge of Cerberus.In FFVII you can see her in the waterfall cave west the Gold Saucer, and southwest of North Corel. Have Vincent in your party and a scene will happen.
- She is still alive. Lucretia had an abundance of Jenova cells that prevented her from taking her own life. What you see is Lucretia in suspended animation, but it seems as though she still maintains some level of function. We see her shed a tear in Dirge and she mumbles a few times, as well.