Preheat oven to 450 degrees F.
Heat oil in a large skillet over medium heat. Add turkey, onion and garlic; cook, stirring and breaking the turkey up with a spoon, until no longer pink, 5 to 7 minutes. Add tomato, chili powder, lemon juice, cumin and 1/4 teaspoon salt. Continue cooking and stirring until hot, 2 to 3 minutes more. Remove from heat and stir in pico de gallo . Meanwhile, place squash, cut-side down, in a microwave-safe dish and add 2 tablespoons water. Microwave, uncovered, on High until the flesh is tender, 10 to 15 minutes. (Alternatively, place squash halves, cut-side down, on a rimmed baking sheet. Bake in a 400 degrees F oven until the flesh is tender, 40 to 50 minutes.)
Use a fork to scrape the squash flesh from the shells into the pan with the turkey mixture. Add the remaining 1/4 teaspoon salt and stir to combine. Place the shells on a baking sheet and fill with the squash mixture. Top with cheese. Bake until heated through and the cheese is melted, 10 to 15 minutes. Serve, topped with lettuce, avocado and more pico de gallo.