Preheat the oven to 375 degrees. In a large bowl, combine the ground lamb, oats, egg, onion, one minced garlic clove, oregano, lemon zest, salt, and pepper. Mix until just combined and press into a loaf pan.
Bake for 45 minutes until the internal temperature reaches 160 degrees. Let the meatloaf rest for 5 minutes before slicing.
While the meatloaf bakes, cook the orzo in a pot of boiling water according to package directions. Drain and return it to the pot. Stir in half the lemon juice and the olive oil.
In a small bowl, mix the Greek yogurt, grated cucumber, remaining minced garlic clove, remaining lemon juice, and dill to make the tzatziki. Season with a pinch of salt if needed.