For the kebabs: Combine oil, lemon juice, herbs, and garlic. Combine marinade and lamb. Cover, and refrigerate for at least 4 hours (preferably overnight).
Make the tomato relish: Preheat grill to medium-high. (If you are using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for just 3 or 4 seconds.) Brush tomatoes with oil, and season with salt. Grill until charred and softened, about 5 minutes per side. Coarsely chop, then place in a sieve set over a bowl. Let drain for 10 minutes. Discard liquid.
Heat oil in a saucepan over medium heat. Cook shallot until translucent, 3 to 4 minutes. Add water and sugar, and simmer until liquid has reduced by half. Add tomatoes and vinegar, and cook for 2 minutes. Stir in 1/2 teaspoon salt and the cayenne. Let cool.
Make the marinated feta: Combine oil, lemon zest and juice, dill, pink and black peppercorns, and red-pepper flakes in a nonreactive dish. Add feta, and turn to coat. Marinate until ready to serve (no longer than 1 hour or cheese will begin to break down).
Thread lamb and onions onto 8 skewers, alternating. Thread a lemon wedge onto one end of each skewer. Season with salt and pepper. Grill until a meat thermometer inserted into lamb registers 130 degrees for medium-rare and onions and lemons are caramelized, about 5 minutes per side. To serve, place each kebab on top of a whole pita, pull out the skewer, and top lamb with relish. Crumble feta over top.