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 mallet or nutcracker, and remove meat. Set aside meat, and discard claw shells. (Do not use claw shells for sauce; thick shells may damage blender or food processor.)
Break off tails, and cut in half lengthwise using kitchens shears. Remove intestinal vein. Remove meat, and cut into 2-inch pieces. Set aside. Reserve tail shells. Remove carapace shell from legs and body meat by inserting thumbs into body cavity and pulling apart. Cut lobster in half lengthwise. Remove eyes and antennae, and discard. (Reserve all other parts for sauce.)
Remove stems from mushrooms, and reserve for another use. 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. Cover and chill.
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.
NOTE: OK, when it came to killing a live lobster, we took the wimp's way out. Mark Gottwald recommends using a 10-inch chef's knife to sever the lobster's spinal cord, inserting the knife at the point where the tail meets the body. Or you can insert it behind the head. The advantage to this method is that shortening the time between killing a lobster and cooking it will improve the quality of meat. But our test kitchen found the knife method took more guts on the cook's part and a little experience to master. So we opted for killing with boiling water. Be sure not to cook the meat at this point, or it may become tough. If you would rather not kill the lobsters yourself, have the seafood market steam them for 2 to 3 minutes only.