Combine ground lamb with oregano, salt, and pepper in a medium-sized bowl. Mix until evenly distributed.
In a food processor, blend parsley, mint, basil, jalapeño, garlic, and lemon zest (from two to three 2-inch strips of peel) until finely chopped.
Mix the herb blend and feta cheese into the lamb mixture. Combine gently to avoid overworking the meat. Divide the mixture into four equal parts and shape each into a patty.
Before cleaning, preheat your grill to 450°F (230°C) and lightly oil the grill grates. Grill the patties for 3 minutes on each side with the lid closed, then an additional 1 minute uncovered. Let the patties rest for 10 minutes before serving them.
Serve your grilled lamb burgers with your favorite topping. For really authentic lamb burgers, I recommend using with tabouli and tzatziki