In a medium bowl, combine 1 cup ricotta cheese, 1 large egg, 1/2 cup shredded mozzarella, 1/2 cup grated Parmesan, 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 mixed and set aside.
Press the Sauté button on the Instant Pot. When the display reads "Hot," add 1 tablespoon olive oil to the inner pot.
Add 1 pound ground beef (or ground chicken or Italian sausage). Cook unmoved for 1–2 minutes, then break the meat up with a wooden spoon and cook until no longer pink.
Add 1 small diced onion, 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 soft. Transfer the cooked meat mixture to a bowl and set aside.
Pour 1 1/2 cups water into the inner pot and use a spatula to scrape and loosen any browned bits from the bottom (deglaze). Turn the Instant Pot off.
Prepare a 7x3-inch springform pan or a push pan. Start assembling the lasagna in this order: a. First layer: break about 3–4 no-boil lasagna noodles as needed to cover the bottom of the pan. b. Second layer: spread about 3/4–1 cup of the 24-oz pasta sauce over the noodles, smoothing with the back of a spoon so the noodles are well covered. c. Third layer: spread half of the meat mixture evenly over the sauce. Press slightly. d. Fourth layer: spread half of the ricotta cheese mixture evenly over the meat. Press slightly.
Repeat step 6 (first through fourth layers) using more noodles, about 3/4–1 cup sauce, the remaining meat mixture, and the remaining ricotta cheese mixture.
Add a final layer of no-boil lasagna noodles to cover the top. Press slightly, spoon remaining pasta sauce over the noodles to cover, and sprinkle 1/2 cup shredded mozzarella cheese evenly on top.
Spray a sheet of aluminum foil with nonstick spray and cover the pan with the foil so it does not touch the cheese (aim for the foil to be about 1 inch above the top layer).
Confirm the inner pot contains the 1 1/2 cups of water you added when deglazing. If you removed it earlier, add 1 1/2 cups water to the inner pot now.
Place the covered lasagna pan on a trivet with handles and lower the trivet into the Instant Pot.
Close and lock the lid. Set the steam valve to Sealing. Press Pressure Cook or Manual and set the cook time to 22 minutes.
When the cooking cycle ends, allow a 15-minute natural pressure release. After 15 minutes, carefully turn the steam valve to Venting to release any remaining pressure, then open the lid.
Using oven mitts, transfer the lasagna pan to a cooling rack.
Preheat the oven broiler to 450°F and place a rack in the middle of the oven. Remove the foil from the lasagna, sprinkle the remaining 1/2 cup shredded mozzarella over the top, and, wearing oven mitts, place the pan under the broiler. Broil just a few minutes until the cheese is bubbly and golden brown—watch closely to avoid burning.
Remove the lasagna from the oven and let it rest on the cooling rack for 10–15 minutes to help it set.
Release the lasagna from the springform pan and slide it onto a serving plate. If using a push pan, wear oven mitts, place the pan on a large can, press the sides of the pan to release the bottom so the lasagna rests on the can, and quickly slide a plate under the lasagna.
Slice and serve.