Mix juice, zest, barbecue sauce, and soy sauce in a small bowl and set aside half for serving with cooked burgers. Combine next 5 ingredients and shape into 12 patties, using around 1/4 cup of meat mixture for each.
Cook patties on griddle over medium-high heat 10 minutes or until they register at 165ºF, turning and brushing occasionally with reserved barbecue sauce mixture.
Fill rolls with lettuce and burgers, and top with remaining reserved barbecue sauce.