In a saucepan, heat the oil over medium heat; add the onions and simmer until soft and melted, 5 to 7 minutes. Add the ketchup, vinegar, Worcestershire sauce, mustard, black pepper, brown sugar, cayenne pepper and lemon juice. Bring to a boil, decrease the heat to low and simmer until the flavors have smoothed and mellowed, at least 10 and up to 30 minutes. Taste and adjust for seasoning with salt and pepper. Store in an airtight container in the refrigerator up to 6 weeks.