Preheat the oven to 400.
Heat a large skillet pan over medium heat. Add the chopped onion, italian sausage and ground beef. Cook the meat, breaking it up as it browns. Add the garlic and continue cooking until the meat is cooked through.
Add the jars of tomato sauce, italian seasoning, and vinegar to the ground meat. Season with salt and pepper. Stir everything together until combined.
Turn the heat to low and simmer the meat sauce uncovered while you prepare the other ingredients.
Chop the zucchini and yellow squash and set aside. You can also do this while the meat is cooking.
Combine all of the ricotta cheese ingredients in a large bowl. Stir well to combine.
Get a large dutch oven, and layer all lasagna ingredients, starting with meat sauce, then vegetables, then ricotta, and then grated cheese. Continue layering until you have used all of the ingredients, and finish it off with a nice layer of cheese on top.
Cover with a lid, and bake for 30 minutes. Remove the lid, and cook for an additional 20 minutes. The lasagna soup should be bubbling and the veggies should be tender.
Serve warm, topped with fresh basil if desired and with a slice of crusty bread!