Split the lobster in two, shell and all, from head to tail with a heavy knife. (If you have par-boiled the lobster, be careful, and this will release lots of hot water when the shell cracks open; make sure to drain the animal well.) Then drizzle the insides of the animal with a mixture of olive oil, lemon juice, salt and pepper, and let it marinate for just a few minutes.
Grill the lobster halves, cut side down, for 5 minutes, then cut side up (adding a bit more marinade) for another 5 minutes. The exact timing will depend, of course, on the size of your lobster; for doneness, check to see that the tail flesh is opaque and quite firm to the touch.
Now serve the lobster in its shell, with a bit more marinade drizzled on top. A large lobster should serve two people if served as part of an Italian-style meal of multiple courses. A small lobster feeds one.