Step 1Heat the grill to medium-high.
Step 2Cut the lobster tails in half lengthwise. Brush all sides of the tails with the olive oil. Grill the tails flesh side down for 5 minutes. Turn and grill until the lobster is opaque in the center, about 5 minutes. When cool enough to handle, remove the lobster meat from the shells and cut into 1-inch chunks. Lightly season with salt.
Step 3Line 4 martini glasses with a lettuce leaf. Stand an avocado quarter in each glass. Divide the lobster among the glasses. Top the lobster with the tomato, corn and cilantro. Thread each of 4 small wooden skewers with a lemon wedge, lime wedge and olive. Garnish each glass with a skewer.