Preheat your oven to 325°F (163°C).
In a large mixing bowl, combine the ground lamb and ground beef. Mix thoroughly to ensure the meats are well integrated.
Add the chopped fresh oregano, minced garlic, and grated onion to the meat mixture. Mix until the ingredients are evenly distributed throughout the meat.
Season the mixture with salt, black pepper, cumin, coriander, nutmeg, and cinnamon. Mix again until all the spices are fully incorporated.
Transfer the meat mixture to a food processor, and process until it forms a fine paste, approximately 1 minute.
Press the meat mixture into a loaf pan, making sure to compact it to remove any air pockets.
Bake in the preheated oven for 60 minutes, or until the internal temperature reaches 165°F (74°C).
Remove the gyro meat from the oven and let it rest for 10 minutes before slicing thinly.
Optionally, for added texture, sear the slices in a hot skillet for 1-2 minutes per side or until edges are crispy.