Preheat the oven: Heat the oven to 425°F. Lightly drizzle a large sheet pan with olive oil.
Mix the meatball mixture: Add the ground beef, ground lamb, parsley, dill, mint, red onion, garlic, cumin, oregano, red pepper flakes, salt, and black pepper to a large mixing bowl. Gently mix with your hands until everything is evenly combined. Avoid overmixing, which can make the meatballs dense.
Shape the meatballs: Use a cookie scoop or tablespoon to portion the mixture. Roll each portion gently between your palms and arrange the meatballs on the prepared sheet pan, leaving a little space between them.
Bake: Place the meatballs in the oven and bake for 15–20 minutes, or until browned and the internal temperature reaches 160°F for ground beef and lamb. If you prefer to follow a 165°F food-safety target, cook until they reach 165°F.
Make the tzatziki: While the meatballs bake, add the cucumber, garlic, and fresh dill to a food processor. Pulse until finely chopped.
Combine the sauce: Transfer the cucumber mixture to a bowl and stir in the Greek yogurt, lemon juice, and salt until smooth and well combined. Refrigerate until ready to serve.
Serve: Let the meatballs rest for a few minutes after baking. Serve warm with plenty of chilled tzatziki.