Add the ham, onion, celery, dijon mustard and 1/3 cup mayonnaise to the bowl of a food processor, pulse several times until ham is a spreadable consistency. If the mixture is too dry add 2-3 more tablespoons of mayonnaise and blend again. Add the lemon zest, brown sugar and hot sauce and blend again until well combined.
Transfer to a bowl and stir in the whole grain mustard and 1 tablespoon lemon juice. Serve as a sandwich spread or on crackers.