Place the onion in a food processor and process until finely chopped. Scoop the onions onto the center of a towel, gather up the ends of the towel and squeeze out the liquid from the onions. Place the onions into a mixing bowl along with the lamb and beef. Season with the garlic, oregano, cumin, marjoram, rosemary, thyme, black pepper and salt. Mix well with your hands until well combined. Cover and refrigerate for 1-2 hours to allow the flavours to develop.
Preheat oven to 165 degrees C.
Place the meat mixture into the food processor and pulse for about a minute until finely chopped and the mixture feels tacky. Pack the meat mixture into a 18 x 10cm loaf pan, making sure there are no air pockets. Line a roasting pan with a damp kitchen towel. Place the loaf pan on the towel inside the roasting pan and place into the preheated oven. Fill the roasting pan with boiling water to reach halfway up the sides of the loaf pan.
Bake until the gyro meat for 45-55 minutes or until the meat is no longer pink in the centre and the internal temperature registers 75 degrees C on a meat thermometer. Pour off any excess fat and allow to cool slightly before slicing thinly and serving.