In a bowl, combine the ground beef, lamb, egg, 1/2 onion, 3/4 cup parsley, egg, cumin, tomato sauce/paste, lemon, olive oil, and salt and pepper. Form into burger patties and set aside.
Heat the grill to medium high heat.
Grill the losh kebab burgers, flipping only once. You can grill these medium rare, or well, depending on your preference. Set aside to rest.
Chop the other onion and parsley. Combine well in a bowl.
Place a burger in a pita wrap, top with onion/parsley mixture, wrap it up, and enjoy!