Place the romaine, kale, radicchio, chickpeas, avocado, and red onion on a cutting board. Top with shaved Parmesan, if using, and squeeze with lemon juice. Season with sprinkles of salt and pepper.

Drizzle generously with the dressing and roughly chop everything on the cutting board, mixing it together as you chop.

Load the salad mixture into the tortilla and fold to close. Serve with more dressing on the side.