Le Mini Club in Marigot has a Lobster buffet on Wednesday and Saturday starting at 6:00 pm. We did it both nights while in SXM, and would definitely do it on our next visit.
A word to the wise, they first bring out chilled lobsters (whole, but cut in half), then about a half hour later, they bring out the fresh off the grill lobster (also cut in half-lengthwise). If you can hold out, wait for the hot grilled ones- They are superb !!!