In a frying pan, heat 1 T. oil over medium heat. Add the summer squash and zucchini and cook until softened, stirring occasionally. Remove from skillet to a plate covered with a towel or paper towel and blot off excess moisture.
Heat 1 T. oil in a 12-inch cast iron skillet over medium heat. Add the onion and cook,until softened, stirring occasionally, about 5 minutes. Season with salt and pepper. Stir in the garlic, pepper flakes, and Italian seasoning and cook until fragrant, about 30 seconds.
Add zucchini mixture to skillet.
Add veggie ground beef to the skillet. Cook, stirring often until warm.
Scatter the pasta in the skillet, then pour the crushed tomatoes and diced tomatoes over the top. Stir, increase the heat to medium-high, and cover. Cook at a bubbling simmer, stirring often, until the pasta is tender, 20 minutes. Keep the pan covered when not stirring. If the lasagna seems dry, you can add a bit of water at the halfway point. Stir the noodles frequently to keep them from clumping together or sticking to the bottom of the skillet.
Preheat the broiler. Remove the skillet from heat. Stir in half the mozzarella, all of the Parmesan, and half of the ricotta. Dot the remaining ricotta over the noodles in tablespoons, then sprinkle with the remaining mozzarella.
Transfer to the oven and broil until the cheese melts and is starts to brown.
Remove from oven and let cool for 15 minutes. Sprinkle with basil and serve.