The best lobster I've ever had on a cruise ship was on Regal Empress five years ago. It was a Canada/New England cruise, and the lobsters were brought on board in Portland, Maine. (We watched as they were loaded on board). Soon after sitting down to dinner, the lights in the dining room were dimmed, and the waiters paraded out, each carrying a tray holding a live lobster. When dinner came, it was a freshly boiled, WHOLE lobster.
To answer the original question, once onboard, you may ask the maitre d' as to the night lobster will be served.