Preheat the oven to 350°F with a rack in the center position.
Place the onion in the center of a clean kitchen towel and wring it out.
Transfer the onion to a large bowl and add the lamb, beef, minced garlic, oregano, cumin, garlic powder, thyme, salt, pepper, and olive oil. Mix well with wet hands.
Transfer the meat mixture to the base of a food processor and pulse until a paste forms, about 2 minutes.
Press the meat mixture firmly into a 9x5-inch loaf pan.
Bake until the internal temperature reaches 165°F on an instant-read thermometer, about 50-60 minutes.
Let the meat cool for 20-30 minutes, then slice very thinly.
