PREHEAT both burners of barbecue to medium-high heat. Cut lemons in half. Squeeze juice into small bowl. Reserve lemon halves for later use. Add barbecue sauce and seasoning to lemon juice; mix well.
TRIM the excess fat from chickens and discard. Place 2 lemon halves and 2 garlic cloves inside the cavity of each chicken.
TURN off burner on one side of barbecue, then place chickens, breast side up, on that side. Cover barbecue with lid. Cook for 1-1/2 to 2 hours or until juices run clear and meat thermometer inserted into thickest part of thighs registers 180°F. During last 20 minutes of cooking, occasionally turn and brush chickens with barbecue sauce mixture. Discard the lemons and garlic from chicken cavities before serving.