Preheat the oven to 375 degrees and lightly grease a 9-by-9-inch baking dish with the olive oil.
Bring a large pot of salted water to a boil and cook the lasagna noodles until just tender. Drain and set aside.
In a mixing bowl, stir together the ricotta, 1 cup of the mozzarella, 1/2 cup of the parmesan, the fontina, chopped basil, salt, and pepper until evenly combined.
Spread 1 cup of marinara sauce across the bottom of the prepared dish. Lay 4 noodles over the sauce, trimming if needed to fit.
Spread half the cheese mixture over the noodles, then top with 1 cup of marinara. Repeat with the remaining noodles, cheese mixture, and 1 cup of marinara.
Sprinkle the remaining 1 cup mozzarella and 1/2 cup parmesan over the top. Arrange the whole basil leaves across the surface.
Cover the dish with foil and bake for 25 minutes. Remove the foil and bake 10 minutes more until the cheese is golden and bubbling at the edges. Let rest 10 minutes before slicing.