Preheat the oven to 375°F (190°C).
Greek Meatballs: In a bowl, combine ground beef, ground lamb, breadcrumbs, red onion, minced garlic, beaten egg, oregano, cumin, salt, and black pepper.
Shape the mixture into meatballs, about 1 inch in diameter.
Heat olive oil in a skillet over medium heat. Brown the meatballs on all sides.
Transfer the meatballs to a baking sheet and finish cooking in the preheated oven for about 10 - 12 minutes or until cooked through.
Make the Garlic sauce: In a food processor blend the olive oil, garlic, lemon juice, salt, and black pepper until very smooth. Set aside.
Arrange tomato and avocado slices. Drizzle with olive oil, sprinkle with dried oregano, garlic, and add a pinch of salt.
Prepare Pita Bread: Warm the pita bread in the oven or on a skillet.
Serve meatballs with tomato and avocado, feta cheese, garlic sauce, Greek olives, and pita bread on the side. Enjoy with a soda, over ice if desired.