Bring 3 quarts water to a boil in a large pot.
Prepare lobsters by plunging them one or two at a time head first into boiling water.
Boil each lobster only long enough to kill it without cooking the meat--about 2 to 3 minutes.
Break off large claws. Crack claw shell with a nutcracker, and remove meat.
Break off tails, and cut in half lengthwise using kitchens shears. Remove all the meatless parts like the antenna, the shell..
Brush mushroom caps with 1 tablespoon oil. Broil 5 inches from heat. Cool and cut into 2-inch pieces.
Thread lobster meat, mushrooms, and tomatoes on skewers. Brush with remaining 2 tablespoons oil, and sprinkle with salt and pepper.
Grill kabobs, without grill lid, over medium-high heat (350° to 400°) 2 to 3 minutes on each side or until lobster meat is opaque. Serve with Lobster Tamarind Sauce.