In a small bowl, combine the paprika, 1 teaspoon sugar, 1 teaspoon salt, garlic powder, thyme, lemon pepper, cayenne and 1/2 to 1 teaspoon pepper; sprinkle over both sides of chicken. Set aside. , In another bowl, combine the mayonnaise, water, vinegar, and the remaining sugar, salt and pepper; cover and refrigerate 1 cup for serving. Save remaining sauce for basting., Grill chicken, covered, over indirect medium heat for 4-6 minutes on each side or until a thermometer reads 170°, basting frequently with remaining sauce. Serve with reserved sauce.