Preheat grill.
Wash and pat dry the tuna steaks. Brush both sides of the steaks with olive oil and season with salt and pepper.
Place tuna and lemon halves on preheated grill and sear each side for 2 minutes for rare. Do not move the tuna around. Allow it to get the char marks.
Slice tuna across the grain into 1/2" thick slices and place on serving platter. Drizzle with lemon juice and spread with pesto.
Serves 2.