In a medium saucepan, mix lemon juice, onion, distilled white vinegar, water, brown sugar, prepared mustard, ground black pepper, salt, cayenne pepper and vegetable oil. Bring to a boil, then simmer uncovered 20 minutes.
Stir ketchup, Worcestershire sauce and liquid smoke flavoring into the mixture. Return to boil, then remove from heat. Refrigerate until ready for use.