Grind the ground chuck and lamb cubes through the coarse plate of a meat grinder twice to mix thoroughly. Place the onion, garlic, marjoram, rosemary, salt, and pepper into a food processor, and pulse until finely ground. Mix together the ground meat and onion mixture in a bowl. Regrind through a fine plate, and pack the mixture into a 3x7 inch loaf pan. Wrap tightly with plastic wrap, and refrigerate overnight.
Preheat an oven to 325 degrees F (165 degrees C).
Remove and discard the plastic wrap from the loaf pan, and bake the gyro meat in the preheated oven until the internal temperature reaches 140 degrees F (60 degrees C), about 1 hour. Drain away all of the liquid that has accumulated in the pan, then remove the loaf from the pan. Place the meat on a rack set above a baking dish to catch the drips, and continue baking until the internal temperature reaches 165 degrees F (75 degrees C), 15 to 30 minutes more. Remove from the oven, and allow to stand 15 minutes before slicing. The finished loaf should be firm and somewhat dry.