Heat the oven to 375°F. Lightly grease 8 wells of a standard muffin pan with some of the olive oil.
In a large bowl, combine the ground lamb, egg, breadcrumbs, feta, red onion, garlic, parsley, oregano, salt, and black pepper. Mix gently just until everything is evenly distributed.
Divide the mixture among the 8 prepared muffin wells. Press it in lightly, leaving the tops slightly rounded. Bake for 20 to 25 minutes, until the muffins are cooked through.
While the lamb muffins bake, bring the chicken broth to a boil in a saucepan. Stir in the orzo, reduce the heat to a gentle simmer, and cook according to the package directions, stirring occasionally, until tender.
Drain any excess broth from the orzo. Stir in the lemon zest, lemon juice, and remaining olive oil.
Let the lamb muffins rest in the pan for 5 minutes, then loosen the edges and lift them out. Serve with the lemon orzo.