Preheat oven to 375°F. Stir together ricotta, eggs, 1/4 cup basil, 2 teaspoons garlic, 1/4 teaspoon salt, and 1/4 teaspoon pepper.
Remove and discard seeds from one-third of the tomato slices. (If tomatoes are particular seedy or juicy, remove seeds from one-half of the tomatoes.) Combine all tomato slices, 1/4 cup oil, vinegar, remaining 2 teaspoons garlic, remaining 1 teaspoon salt, and remaining 1/2 teaspoon pepper in a large bowl; toss gently to combine.
Coat a 13- x 9-inch glass or ceramic baking dish with cooking spray. Arrange one-third of the tomato slices in a single layer on bottom of baking dish; top with 3 lasagna noodles. Spread ricotta mixture evenly over noodles; top with 3 lasagna noodles. Arrange one-third of the tomato slices in a single layer over noodles, and top with remaining 3 noodles. Arrange remaining tomatoes over top, shingling if necessary. Pour any tomato juices from bowl evenly over lasagna. Cover baking dish with foil, and bake at 375°F for 15 minutes.
Meanwhile, place bread in a food processor; pulse until coarse crumbs form, 4 to 5 times. Heat remaining 2 tablespoons oil in a large skillet over medium. Add breadcrumbs; cook, stirring often, until toasted, 3 to 4 minutes. Transfer to a medium bowl; cool 5 minutes. Add cheese and remaining 1/4 cup basil; toss.
Remove lasagna from oven; remove foil. Sprinkle breadcrumb mixture over lasagna. Return dish to oven; bake at 375°F until top is browned, about 10 minutes.