Preheat a grill or grill pan to medium. In a large skillet, heat 2 tablespoons olive oil over medium heat. Add the onion and cook, stirring occasionally, until crisp-tender, 3 to 4 minutes. Stir in the vinegar and sugar.
Rub the remaining 1 tablespoon olive oil on the halibut and season with salt and pepper. Add to the grill, cover and cook, turning once, until firm to the touch and grill marks appear, 7 to 8 minutes.
Stir the strawberries into the onion mixture, then toss with the lettuce; season with salt and pepper. Serve with the fish.
