Unfortunately....

While some lobsters can live down to 700 meters (2300 feet). The Titanic lies 3800 meters (12500 feet) underwater.

There would also be a problem with the cold of the region of water. The temps at the depth of the Titanic are too cold for them to survive.

Lobsters on the Titanic probably had their claws bound. As you can usually see this in markets stores where modern live lobsters have their claws wrapped with rubber bands. So even if they were to survive the crushing depths, and bitter cold, they would have starved or become food for other predators. This sadly would have precluded them from shooting off revolvers while they danced.

There is a fantastic little French novel called Lobster about exactly this.

A lobster survives, after seeing his father be eaten, only to fall in love with the woman who ate his father. The novel is the story of his pursuit and erotic encounter with his father’s devourer.

From goodreads (fuck Amazon):

Aboard the Titanic, Lobster watches Angelina devour his father, before being plucked out of the aquarium himself. Just as he is put in the boiling pot, the ship hits the iceberg and the pot is thrown to the floor. Lobster survives, with some changes: he finds himself sexually attracted not only to a human, but to the very human who ate his father. He gives her one life-changing orgasm before their tragic separation, following an ugly incident in one of the lifeboats.

Death to America, and butter sauce!

i think the lobsters be eat are not the deep sea types, but used to live few 100 meters at most