Using the SAUTE feature on NORMAL, heat the olive oil.
Add the Italian sausage, breaking apart with the back of the spoon. Cook, stirring regularly until it loses its pink and begins to render fat.
Add onions, sweet peppers, and garlic and cook until softened.
Drain the meat of any excess grease.
Break the lasagna into small pieces and place them in the pot on top of the meat.
Add chopped tomatoes (including packing juice), tomato paste, and chicken broth. Gently push down the noodles to submerge in the liquid.
Add Italian seasoning, sugar, and salt and pepper to taste.
Close the lid of the Instant Pot, making sure the valve is on the SEALING position. Press PRESSURE COOK and cook on HIGH pressure for 4 minutes.
When the 4 minutes is up, allow natural release for 5 minutes, and then do QUICK release.
Adjust seasonings with salt and pepper if needed.
Stir the soup to distribute and ladle in serving bowls. Top with Parmesan cheese, ricotta cheese, and mozzarella cheese, if desired.