Dice the ham in very small pieces or use a food processor to grind it to the desired consistency. If using a food processor you can also pulse the celery, onions, and pickles into a fine dice, or use a knife to cut by hand.
Combine ham, celery, pickles, onions, and mustard in a medium-size bowl. Stir in 4 tablespoons of lacto-fermented mayonnaise and add additional mayonnaise as desired.
Store in the refrigerator. Makes enough for 4 hearty sandwiches.