Put root beer, ketchup, lemon zest and juice, orange juice, Worcestershire sauce, brown sugar, molasses, liquid smoke, ginger, garlic and onion powders and pepper in heavy, nonreactive saucepan and gradually bring to boil over medium heat. Reduce heat slightly and gently simmer sauce until thick and richly flavored, 10 to 15 minutes. Taste for seasoning, adding lemon juice, brown sugar or other ingredients as necessary.
Transfer sauce to bowl or clean glass jars and let cool to room temperature. Refrigerate, covered, until ready to serve. The sauce can be served chilled or at room temperature. It will keep, refrigerated and covered, several months.