In a medium bowl, stir together Chobani, mint, garlic, lemon juice, salt, pepper and sugar and set aside.
Liberally season lamb with salt and black pepper. Drizzle some olive oil over both sides of lamb. Heat grill pan over high heat for 1 ½ minutes. Add lamb and grill until browned, 4-5 minutes. Turn lamb over and cook 3-4 minutes for medium-rare. Remove from heat and rest 10 minutes before slicing crosswise against the grain.
Place pita on grill pan and cook on both sides until marked. Transfer 1 pita to each plate and top with some cucumbers and tomatoes. Lay a few pieces of lamb on top and finish with the Chobani sauce.