In a large bowl combine lamb, shallot, 2 teaspoons of the oregano, the cinnamon, salt, pepper, and the water. Form into four 3/4-inch-thick patties. If the lamb mixture is sticky, moisten hands to shape the patties.
Grill patties, covered, directly over hot coals for 4 to 5 minutes per side or until done (160 degrees F), turning once halfway through grilling time. Toast buns, cut sides down, the last 1 to 2 minutes of grilling time.
Meanwhile, for sauce, combine feta, sour cream, and remaining oregano. Serve grilled patties on toasted buns with sauce and, if desired, sliced tomatoes.