Prep the veg - Core and finely slice the cabbage and radicchio (if using) into 1-inch ribbons. Shred the carrot, using the food processor. Destem, deseed, and chop the green bell pepper into a small dice.
Make the dressing - Stir together the mayo, vinegar, lemon juice, sugar, celery salt, and pepper.
Combine - Mix the veg and dressing until the veg is evenly coated, and refrigerate until ready to serve.