Trim external fat on beef brisket to 1/4 inch. Combine paprika and 1/2 tsp. of the black pepper; rub evenly over surface of beef brisket. Place brisket, fat side down, in 11 1/2 X 9" disposable foil pan. Add 1 cup water. Cover pan tightly with aluminum foil. Place in center of grid over very low coals (use a single layer of coals with space in between each); cover cooker. Cook 5 - 6 hours, turning brisket over every 1 1/2 hours; use baster to remove fat from pan as it accumulates. Add 1/2 cup water, if needed, to pan during cooking. (Add just enough briquette during cooking to keep coals at a very low temperature). Remove brisket from pan; place on grid, fat side down, directly over very low coals. Reserve pan dripping. Cover; continue cooking for 30 minutes to 1 hour.
Meanwhile, skim fat from pan drippings; reserve 1 cup drippings. Melt butter in medium saucepan over medium heat. Add onion; cook until tender crisp. Add reserved pan drippings, remaining 1/2 teaspoon black pepper, the catsup, lemon juice, Worcestershire sauce and hot pepper sauce; simmer 15 minutes.
Carve brisket into thin slices across the grain; serve with sauce. Garnish with fresh peppers and lemon and lime slices.
1 each boneless beef brisket -- (6 to 8 pounds)
2 teaspoons paprika
1 teaspoon ground black pepper -- divided
1 tablespoon butter
1 each medium onion -- grated
1 1/2 cups catsup
1 tablespoon fresh lemon juice
1 tablespoon Worcestershire sauce
1 teaspoon hot pepper sauce