Heat the olive oil in the Instant Pot using the saute function. When hot, add the onion and cook, stirring often, for about 2 minutes until softened.
Add the ground beef (or ground turkey) to the Instant Pot and cook, crumbling, until browned. Drain off any excess grease.
Add the garlic to the pot and cook, stirring, for 30 seconds. Turn off the Instant Pot.
Add the Italian seasoning, salt and pepper to the pot and stir to combine.
Remove 2/3 of the meat mixture to a clean bowl, leaving the rest in the pot.
Pour the water into the pot and stir, scraping up any bits that are stuck to the bottom of the pot.
Layer the lasagna: Break 2 of the lasagna noodles in half and lay the 4 halves on top of the water and meat in the bottom of the pot. Put 1/3 of the reserved meat on top of the noodles, followed by 2/3 cup of the marinara sauce and 1/3 cup of the shredded mozzarella.
For the second layer, break 2 more lasagna noodles in half and lay the 4 noodle halves in the opposite direction as the layer below. Top with half of the remaining meat, 2/3 cup sauce and 1/3 cup shredded cheese.
Make another layer with 4 noodle halves (arranged in the opposite direction as the previous layer), the remaining meat, 2/3 cup sauce and 1/3 cup cheese.
For the top layer, arrange the remaining 4 noodle halves and cover with the remaining marinara sauce.
Reserve the remaining shredded mozzarella in the refrigerator while the lasagna cooks.
Close the Instant Pot lid and turn the steam release valve to the sealing position. Set the cook time to 10 minutes at high pressure. The Instant Pot will take about 15 minutes to reach pressure and then the cook time will begin counting down. When the cook time ends, do a controlled quick release of the pressure by slowly turning the steam release valve to the venting position, a little bit at a time, using the handle of a long spoon.
Once all of the steam has been released and the pin drops down, carefully open the Instant Pot lid. The lasagna may look somewhat watery and this is ok. Most of the liquid will be absorbed as the lasagna rests. Sprinkle the reserved mozzarella cheese over the top of the lasagna. Let lasagna rest in the Instant Pot, with the lid off, for 5-10 minutes before serving. (A 10 minute rest is best, if you can wait.)
Serve with grated Parmesan cheese and chopped fresh parsley, if desired.