Remove parts from turkey cavity. Remove and discard fat from just inside the body and neck cavities. Rinse turkey inside and out under cold running water, and pat dry inside and out with paper towels. Rub turkey cavities with both halves of cut lemon, squeezing lemon gently.
Combine kosher salt, pepper, orange zest, and garlic in a small bowl. Rub mixture inside body and neck cavities of turkey.
Gently lift turkey skin from the sides, and slide frozen butter pieces underneath, without breaking the skin. Rub outside of turkey with softened butter.
Tie wings and legs of turkey to the body with kitchen string so they won't scrape against the grill.
Turn all gas grill burners on high for 5 minutes or until grill is hot. Turn off all burners except one, and place a metal drip pan under spit where turkey will cook. Add chopped onion and 1 cup water to drip pan. (The pan will catch drippings and prevent flare-ups.) Place turkey on rotisserie, and secure according to manufacturer's directions.
Start motor; adjust turkey if necessary so it remains balanced for even cooking. Grill turkey, moderating burner if necessary to keep grill temperature at 350°, 10 to 15 minutes per pound or until thermometer inserted in the thickest part of the thigh reads 180° (about 2 to 2 1/2 hours). Baste turkey every 20 to 30 minutes with pan juices. If water in pan starts to evaporate, add more hot water, 1/4 cup at a time.
Remove turkey from grill spit, and place on cutting board. Cover with foil, and let stand 20 minutes before carving.
Meanwhile, pour juices from drip pan into a 4-cup measure. After fat rises to the surface, spoon 1/4 cup of fat into a medium saucepan; discard any remaining fat. Add orange juice and, if necessary, chicken stock to drippings to make 4 cups. Heat saucepan over medium-high heat; add flour, and cook, whisking constantly, 1 minute. Add drippings mixture, and cook, stirring constantly, 5 minutes or until gravy thickens and boils. Season with kosher salt and pepper.