Heat a wide, high-sided nonstick pan over medium heat. Add ground beef, breaking it apart as it cooks. Cook until browned, about 5 minutes.
Add tomato sauce, stirring it in. Bring to a simmer. Simmer for 10 minutes so that the sauce is noticeably thickened, stirring occasionally.
Add oregano, salt, and cayenne. Stir until well-mixed.
Add spinach, stirring for a few minutes until wilted. Turn off the heat.
Assembling & Baking The Lasagna:
Arrange one third of the turkey slices along the bottom of an 8×8 inch baking dish so that they are overlapping. Evenly pour about half of the meat sauce over the turkey slices. Add about 1/2 cup of mozzarella cheese on top of the meat sauce.
Repeat with another sliced turkey layer, a meat sauce layer, and a cheese layer.
Top with remaining turkey slices. Add remaining 1/2 cup mozzarella cheese and 1/4 cup parmesan cheese on top of the turkey slices.
Bake at 375 F until the lasagna is golden brown on top, 30 to 35 minutes. Let it cool for at least 15 minutes to allow the lasagna to set (don’t skip this step) before cutting into slices and serving.
If making ahead: after the lasagna has cooled, cover and refrigerate. When ready to serve, cut into individual portions and reheat.