Prepare all ingredients, including preheating the oven to 325°F (165°C) and greasing a 9x5-inch loaf pan with cooking spray.
In a food processor, pulse the onion into a fine chop, using about five one-second pulses. Place the chopped onion onto a towel, gather the towel ends, and squeeze out any excess moisture.
In a large mixing bowl, combine the squeezed onion, lamb, beef, garlic, oregano, cumin, marjoram, rosemary, thyme, black pepper, and sea salt. Blend thoroughly with your hands until well mixed. Cover the bowl and refrigerate for 1 to 2 hours, allowing the flavors to infuse.
Once chilled, transfer the meat mixture in batches to a food processor and pulse each batch for about 1 minute, until the texture becomes tacky and uniform.
Press the processed meat mixture firmly into the prepared loaf pan, ensuring there are no air pockets. Place a damp towel in a medium roasting pan and position the loaf pan in the center. Pour boiling water into the roasting pan until it reaches halfway up the sides of the loaf pan.
Bake in the preheated oven for approximately 1 hour to 1 hour and 25 minutes, or until an internal thermometer reads at least 160°F (70°C), indicating doneness.
Carefully drain any fat from the pan, allow the meat to cool slightly, then slice thinly.
Serve the gyro meat warm and enjoy.