Mix together paprika, fennel, cumin, coriander, cinnamon, garlic, cayenne, 2 teaspoons salt, and 1/2 teaspoon pepper and then mix into the lamb until spices are evenly distributed (the meat will take on a reddish tone).
Divide meat into 4 patties.
Preheat a grill to medium-high and lightly oil the grates. Cook burgers for about 4-5 minutes per side, or until an instant-read thermometer reads 140°F. Let the burgers rest while preparing the sauce.
To make the sauce, mix yogurt, cucumber, mint, salt, pepper, and lemon juice together. Serve over burgers.
Notes
Stovetop instructions: Heat a skillet over medium-high. Cook burgers, in batches if needed, for about 5 minutes per side.