Warm oil in a 12-inch nonstick skillet over medium-high heat. Add garlic and cook until fragrant, 30 seconds to 1 minute. Add turkey, salt and pepper and cook, breaking up meat into small pieces with a wooden spoon, until it loses its pink color, 3 to 5 minutes.
Scatter lasagna noodles over turkey. Pour tomato sauce and 2 cups water on top of noodles. Bring to a simmer, and then reduce heat to low, cover and cook at a low boil until noodles are tender, stirring occasionally, 20 to 22 minutes. Season with more salt and pepper, if desired.
Sprinkle 1 cup mozzarella onto turkey and noodle mixture and stir to combine. Remove pan from heat and spoon heaping tablespoonfuls of ricotta on top of lasagna. Sprinkle with remaining mozzarella. Cover and let stand until mozzarella is melted, 4 to 5 minutes. Serve hot.