1. Place turkey breast and thigh in a shallow container in the freezer for 30 minutes to facilitate grinding. Attach the food grinder, with the coarse plate, to the grinder. Set to speed 4 and run turkey through the grinder into a large bowl. Sprinkle with lemon zest, lemon juice, thyme, salt and pepper; mix together with your hands. Freeze for 30 minutes, then run through the grinder one more time into a bowl. Add bread crumbs and mix together with your hands. Form into 8 patties, each about 1 inch (2.5 cm) thick, creating a slight depression in the middle of each one to ensure even cooking.

2. In a large skillet with a lid, heat a thin layer of oil over medium heat. Add 4 of the patties. Cover and cook, flipping once, until no longer pink inside, about 4 minutes per side. Top each patty with cheese, if desired. Cover and cook until just melted. Transfer to a plate and keep warm. Repeat with remaining patties.

3. Serve on buns, topped with mayonnaise, red onion and lettuce.