Prepare the tuna salad:
In a medium bowl, combine the drained tuna, mayonnaise (or Greek yogurt), Dijon mustard (if using), red onion, celery, cucumber (optional), lemon juice, salt, and pepper. Mix everything together until well combined. Taste and adjust seasoning as needed.

Assemble the wraps:
Lay the tortillas flat on a clean surface. If you like, you can warm them up slightly in a dry skillet or microwave for a few seconds to make them more pliable.

Add the fillings:
Evenly distribute the mixed greens and avocado slices (if using) onto each tortilla. Spoon a generous amount of tuna salad on top of the greens, then sprinkle with shredded cheese if desired.

Wrap it up:
Fold the sides of the tortilla in, then roll it up tightly from the bottom to secure the filling. Slice the wraps in half on the diagonal for easy eating.

Serve:
Serve immediately, or wrap in foil or plastic wrap for a packed lunch or picnic. Enjoy with your favorite dipping sauce or a side of fresh veggies!