Prepare the vegan chicken salad: In a bowl, combine the shredded vegan chicken, vegan mayonnaise, celery, red onion, dill, lemon juice, salt, and pepper. Mix well.
Soften the rice paper wrappers: Dip one rice paper wrapper in warm water for a few seconds until softened.
Assemble the summer roll: Lay the softened wrapper on a flat surface. Place a small amount of lettuce and carrots in the center. Top with a few spoonfuls of the vegan chicken salad and mint leaves.
Fold the sides of the wrapper inward, then tightly roll from the bottom up.
Repeat with the remaining wrappers and filling.
Serve immediately or chill for later.
Notes
Adjust the amount of vegan mayonnaise to your liking.
Add other vegetables like cucumber or bell peppers.