Bring a large pot of lightly salted water to a boil. Cook lasagna in boiling water until cooked through but firm to the bite, about 8 minutes; drain and lay noodles flat onto a flat surface.
Heat olive oil in a skillet over medium heat. Cook and stir garlic in hot oil until fragrant, about 2 minutes. Transfer garlic to a large bowl; add spinach, ricotta cheese, mozzarella cheese, and salt. Stir mixture until evenly combined.
Spread a heaping 1/4 cup of spinach mixture into the middle of each lasagna noodle. Roll noodle firmly around the filling. Arrange rolled noodles into a baking dish. Pour spaghetti sauce over the rolls. Cover dish with aluminum foil.
Bake in preheated oven for 30 minutes. Remove foil from dish and continue cooking another 5 minutes. Sprinkle Parmesan cheese over the rolls to serve.