Lucrecia definitely has Jenova cells, a result of the experiments she took part in. She even says this when you encounter her in the waterfall cave in the original game, part of the side-quest that helps to explain Vincent's past and provide his ultimate weapon and limit break.
She says she's overwhelmed with guilt because of what she did, "but the Jenova cells in me won't let me die", or words to that effect. She can feel Sephiroth's existence, so she's got some of the Reunion instinct going. I'd guess the strong and rational side of her mind was enough for her to resist the full impact of the cells, just like SOLDIER members can.

In Dirge of Cerberus, it seems that her body's been entombed in the naturally-occurring Materia crystals of the cave. She's no longer truly alive or dead, though - she can whisper apologies to Vincent in a way that might be slightly telepathic, but her spirit's also begun returning to the Lifestream, which is proven when (SPOILER)Shelke retrieves the Protomateria from her, inside Omega.

FFVII provides more answers than DoC, though you have to complete Vincent's side-quest to get them.