Rinse fish, and pat dry. Cut 1/2-inch-deep vertical slits on each side, about 1 inch apart. Rub lime halves thoroughly on inside and outside of fish.
Dredge fish in cornstarch; hold by the tail, and shake to remove excess.
Pour oil to cover in a large skillet or roasting pan; heat to 350° over medium-high heat.
Fry fish for 8 to 10 minutes on each side. Drain on paper towels.
Transfer fish to a platter; arrange lettuce and next 3 ingredients around fish. Serve immediately with remaining ingredients.
Note: We tested with red snapper, but you can substitute striped bass. Instead of frying, you can bake the whole fish for 40 minutes at 350º. Omit dredging fish in cornstarch.