In a medium bowl, combine the cheese layer: 1 cup Ricotta cheese, 1 large egg, 1/2 cup Mozzarella cheese (shredded), 1/2 cup Parmesan cheese (grated), 1 teaspoon dried basil, 1 teaspoon dried thyme, 1 teaspoon dried oregano, 1 teaspoon Italian Seasoning, 1/4 teaspoon red pepper flakes, 1/4 teaspoon salt, and 1/4 teaspoon ground black pepper. Stir until evenly combined and set aside.
Turn the Instant Pot to Sauté. When it reads hot, add 1 tablespoon olive oil to the inner pot.
Add 1 pound of your chosen meat (ground beef or ground chicken or ground Italian sausage) to the pot. Let it cook undisturbed for 1–2 minutes, then break it up with a wooden spoon and continue cooking until no longer pink.
Add 1 small onion (diced), 1 tablespoon minced garlic, 1/4 teaspoon salt, and 1/4 teaspoon ground black pepper to the meat. Sauté, stirring occasionally, for 1–2 minutes, until the onion is softened.
Scoop the cooked meat mixture into a bowl and set aside.
Pour 1 1/2 cups water into the empty Instant Pot inner pot and use a spatula or wooden spoon to scrape and deglaze the bottom. Turn the Instant Pot off after deglazing. Leave the 1 1/2 cups of water in the pot.
Prepare your 7x3 springform pan or push pan (or a similarly sized pan that fits inside your Instant Pot trivet). If using foil to cover, spray one side of a sheet of foil with nonstick spray so the foil will not stick to the cheese later.
Assemble the lasagna in the pan using the 9 No-boil lasagna noodles and the 24 oz jar pasta sauce as follows: a. First layer: Break about 3–4 of the no-boil noodles as needed and arrange them to cover the bottom of the pan. b. Second layer: Spread about 3/4–1 cup of the pasta sauce over the noodles, smoothing to cover the noodles. c. Third layer: Spread half of the reserved meat mixture evenly over the sauce. d. Fourth layer: Spread half of the cheese mixture evenly over the meat. e. Repeat layers a–d (noodles, 3/4–1 cup sauce, remaining meat, remaining cheese). f. Final top noodle layer: Add a final layer of no-boil noodles. Press gently to compact. g. Cover the top noodles with remaining pasta sauce. Sprinkle 1/2 cup of the 1 cup Mozzarella cheese (shredded) over the sauced top.
Cover the pan with the sprayed foil so the foil does not touch the cheese; aim for about a 1-inch gap between foil and the top of the lasagna.
Place a trivet with handles into the Instant Pot inner pot. Using oven mitts if needed, set the covered lasagna pan on the trivet and carefully lower both into the Instant Pot on top of the 1 1/2 cups of water.
Close and lock the Instant Pot lid. Turn the steam release knob to Sealing. Press Pressure Cook or Manual and set the time to 22 minutes.
When the cook cycle ends, allow a 15-minute Natural Release. After 15 minutes, turn the steam release knob to Venting to release any remaining steam, then open the lid.
Using the trivet handles or oven mitts, carefully lift the lasagna pan out of the Instant Pot and place it on a cooling rack.
Preheat the oven broiler and position an oven rack in the middle of the oven (set broiler to about 450°F if your oven indicates a temperature).
Remove the foil from the lasagna. Sprinkle the remaining 1/2 cup of Mozzarella cheese (shredded) evenly over the top.
Place the lasagna (in its pan) under the broiler for a few minutes, watching closely, until the cheese is bubbly and golden brown. Use oven mitts when handling the hot pan.
Remove the lasagna from the oven and let it rest on a cooling rack for 10–15 minutes to help it set.
Release and remove the lasagna from your pan: for a springform pan, unclip the ring and lift it away; for a push pan, follow the pan manufacturer’s instructions (you can lift and press the sides away from the base, or invert carefully onto a plate as appropriate).
Slice and serve.