For the kofta: Add the frozen lamb shoulder and breast cubes to a food processor and pulse until a ground meat mixture is formed. Alternately, use a meat grinder. Place the ground lamb in a mixing bowl and sprinkle with the chili powder, cumin, sumac, salt and pepper. Using wet hands, form into 8 oval patties.
Add the oil to a Dutch oven fitted with a deep-frying thermometer and bring the temperature of the oil up to 375 degrees F. Place a rack in a sheet pan. Place the patties in the hot oil in batches and fry until cooked through, 3 to 5 minutes. Drain on the rack.
For the sauce: Combine the sodium citrate with 1/4 cup water in a small saucepan and stir to dissolve. Place over medium heat along with the milk and feta. Bring to a simmer, then turn off the heat and blend into a sauce using an immersion blender.
To serve: Place a kofta patty inside half of a pita and top with cucumber slices, a drizzle of some feta sauce and some dill. Repeat with the remaining ingredients to make 7 more.