Put the onion in the bowl of a food processor and process for 10 to 15 seconds. Turn the chopped onion out into the center of a tea towel. Gather up the ends of the towel and squeeze until almost all of the juice is removed. Discard juice.
Return the onion to the food processor and add the lamb, garlic, marjoram, rosemary, salt, and pepper, and process until it is a fine paste, approximately 1 minute. Stop the processor as needed to scrape down sides of bowl.
To cook in the oven as a meatloaf: Heat oven to 325ºF. Place the mixture into a loaf pan, making sure to press into the sides of the pan. Place the loaf pan into a water bath and bake until the mixture reaches an internal temperature of 165 to 170ºF, 60 to 75 minutes. Remove from the oven and drain off any fat. Place the loaf pan on a wire rack and place a brick wrapped in aluminum foil directly on the surface of the meat and allow to sit until the internal temperature reaches 175ºF, 15 to 20 minutes. Slice and serve on pita bread with tzatziki sauce, chopped onion, tomatoes, and feta cheese.
To cook on a rotisserie: Form the meat mixture into a loaf shape and place on top of 2 overlapping pieces of plastic wrap that are at least 18 inches long. Roll the mixture in the plastic wrap tightly, making sure to remove any air pockets. Once the meat is completely rolled in the wrap, twist the ends of the plastic wrap until the surface of the wrap is tight. Store in the refrigerator for at least 2 hours or up to overnight to allow the mixture to firm up.
Heat grill to high.
Place the rested meat onto the rotisserie skewer. Fold a double layer of aluminum foil into a tray and place directly under the meat to catch any drippings. Cook on high for 15 minutes. Decrease the heat to medium and continue to cook until the internal temperature of the meat reaches 165ºF, another 20 to 30 minutes. Turn off the heat and let the meat continue to spin until the internal temperature reaches 175ºF, another 10 to 15 minutes. Slice and serve on pita bread with tzatziki sauce, chopped onion, tomatoes, and feta cheese.