In a medium saucepan, combine catsup, brown sugar, granulated sugar, cooking oil, vinegar, honey, and Worcestershire sauce. Stir over medium heat until the sugars dissolve and sauce is hot. Cover and refrigerate up to 1 week.
Combine ground pork and sausage seasoning in a large mixing bowl. Form mixture into four 3/4-inch-thick patties.
For a charcoal grill, place patties on the grill rack directly over medium coals. Grill, uncovered, for 14 to 18 minutes or until an instant-read thermometer inserted into the center of a patty registers 170 degrees F. Turn patties halfway through cooking time and brush with sauce.
For a gas grill, preheat grill. Reduce heat to medium. Place patties on the grill rack; cover and grill as directed in step 3.
Serve patties on Texas toast or buns topped with lettuce and onion slices. Pass additional sauce. Makes 4 servings.