Heat the oven to 375°F. Lightly grease 8 cups of a standard muffin tin.
In a large bowl, combine the ground lamb, breadcrumbs, egg, red onion, garlic, parsley, oregano, salt, black pepper, and lemon juice. Mix gently just until everything is evenly combined.
Divide the lamb mixture among the 8 prepared muffin cups. Press it in lightly without packing it too tightly. Bake until the centers reach 160°F, about 20 to 25 minutes.
While the muffins bake, place the potatoes in a saucepan and cover them with cold water. Bring to a boil, then simmer until the potatoes are tender when pierced with a fork, about 15 to 20 minutes. Drain well.
Return the potatoes to the warm saucepan. Add the milk, butter, and half of the feta. Mash until smooth and creamy.
Let the lamb muffins rest in the tin for 5 minutes, then transfer them to a serving plate. Spoon or pipe the feta mashed potatoes over each muffin and finish with the remaining feta.