After acquiring the submarine or a Gold Chocobo, you can reach Lucrecia's Cave, which is located behind a waterfall in a lagoon in the Nibel area. To reach it by submarine, you must come through an underwater cave just east of the lagoon and park against the rocky ledge left of the waterfall. The Gold Chocobo can simply ride over the mountains, but you must dismount it near the ledge.
Visit the cave during Disc 2 with Vincent in your party. You'll learn a lot more about Vincent's life and how he got locked in a coffin in the Shinra Mansion's basement. During Disc 3, revisit the cave with Vincent in your party to find his ultimate weapo, Death Penalty, and his Chaos Limit Break.