Divide ground lamb equally into 4 portions weighing roughly 5 ½ ounces each. Flatten into uniform rounds, then use your thumb or finger to make a small indentation right on top in the center of each patty.
Prior to cooking, sprinkle each patty generously with kosher salt and freshly ground black pepper (about ¼ tsp each) on both sides.
Combine all sauce ingredients in a large bowl, then whisk to combine. Refrigerate until needed.
Preheat a grill, cast iron skillet, or griddle over medium-high heat. Coat with nonstick oil spray. Cook each burger patty for 5 minutes per side. Allow burgers to rest before serving on buns with herbed yogurt sauce and additional toppings.