In a medium bowl, mix together the onion, garlic, parsley, mint, mustard, horseradish, Worcestershire, salt, cumin, pepper and egg. Add the lamb and mix well with your hands.
Shape the lamb mixture into 4 patties. Press 1 tablespoon of the blue cheese into the center of each patty; roll into balls and then flatten into 3-by-1-inch patties. Transfer to a plate and refrigerate, uncovered, for at least 30 minutes and up to 2 hours.
Heat a large cast-iron skillet over medium heat, then add the butter and canola oil. Place the cold patties in the skillet and cook until browned on both sides and cooked through, 4 to 6 minutes per side for medium-well.
Assemble the burgers: Place the burgers on the buns, and layer with lettuce, red onions and tomatoes.