Prepare a medium-high gas or charcoal grill fire. In a large bowl, thoroughly mix the lamb with 1 Tbs. of the olive oil, the coriander, cumin, ginger, cinnamon, 1-1/2 tsp. salt, and 1/4 tsp. pepper. Form into four 1/2-inch-thick burgers.
Oil the grill grate. Grill the burgers for 5 minutes, then flip and continue to grill until an instant read thermometer inserted into a burger registers 145°F for medium, about 5 minutes.
Meanwhile, put the remaining 1/4 cup olive oil in a mini food processor with the parsley, cilantro, oregano, vinegar, garlic, red pepper flakes, and 1/4 tsp. salt. Process until a coarse paste forms, scraping the sides of the processor at least once.
Serve each burger in a pita half with the sauce, sliced tomato, and a dollop of yogurt.