On disc 2 after you acquire the submarine you can visit Lucrecia. Travel to the Waterfall Cave, which is in the Nibel area. Get out with Vincent in your party and go into the cave. You'll see a kind of shrine and Vincent will walk towards it.

After Vincent have a chat with Lucrecia,We enter a series of scenes with no dialogue.

- We are back in Nibelhiem, many years ago. There are three scientists in walking toward the Shinra mansion: Hojo, Gast, and Lucrecia.
-They are followed by a man in a Turks uniform, the young Vincent.
- The scene changes to Vincent and Lucrecia walking through Nibelheim Town Square, arm in arm.
- The scene changes to outside the mansion. Vincent is handing something to Lucrecia, (an engagement ring?). Lucrecia starts to cry and runs away shaking her head. Vincent stands and watches helplessly.- The scene changes again and we see Hojo and Lucrecia at
the gate, kissing. Vincent appears, stares sadly a moment, then leaves before they see him
This show Lucrecia rejecting Vincent and chose Hojo instead.

Vincent's Voice - "If she is happy then... I don't mind."
It seems like from Vincent's POV that Lucrecia is happy.

- The scene changes to the top floor of the Nibelheim Inn; Lucrecia has her
head in her hands)
- The scene changes to the laboratory in the basement of the Shinra mansion.
Hojo and Lucrecia stand side by side, on one side of the room, Vincent on the other.)

Vincent - "I'm against it! Why experiments on humans!?"

Hojo - "She and I are both scientists!!"

(The screen goes black.)

Vincent's Voice - "After that, a child was born to Lucrecia...
That child's name is...
Sephiroth..."
This show that Vincent is against the experiment and the sliver hair dude that make million of fanboys and girls wet their pants is born.

- The scene changes back to the top of Nibelheim Inn, Lucrecia collapse on the floor.
- The scene changes back to the laboratory. Vincent and Hojo argue heatedly,
Hojo begins to lose it and in his fury shoots Vincent.
- The scene changes to show Vincent having been tied to an operating table.
Hojo works away on the unconscious Vincent.
- When the scene changes again Hojo is gone and Vincent is alone. He gets up and looks at himself, the shaking he raises both fists to the sky and the scene fades to black.

Vincent - "Urrrrrrrrgh!!"

Vincents Voice - "This body is... the punishment that's been given to me...I was unable...... to stop Professor Gast and Hojo... And Lucrecia... I wasn't unable to stop them...All that I was able to do was watch... That is my punishment..."
This part is bascially about Vincent and things didn't go so well for Lucrecia.

(We are back in the cave with Lucrecia and Vincent.)

Vincent - "Lucrecia... You're alive..."

Lucrecia - "I wanted to disappear... I couldn't be with anyone... I wanted
to die... But the Jenova inside me wouldn't let me die... Lately, I
dream a lot of Sephiroth... My dear, dear child. Ever since he was
born I never got to hold him, even once... Not even once. You can't
call me his mother... That... is my sin..."
This show why Lucrecia is still lurking around in that cave. Later, Vincent will tell her that Sephiroth is dead and she will dissappear.

PS: You can return here in disc 3 to get Vincent's ultimate weapon & limit break.