Prepare the chicken: Chop or shred the cooked chicken into small, bite-sized pieces.
Chop the vegetables: Finely chop the celery and slice the green onions.
Make the dressing: Mix the mayonnaise, lemon juice, Dijon mustard, salt, and black pepper until smooth.
Add the chicken: Add the chicken, celery, and green onion to the dressing.
Mix gently: Stir until everything is evenly coated without overmixing.
Taste the filling: Adjust with more lemon juice, mustard, salt, or pepper if needed.
Chill if desired: Cover and refrigerate for about 30 minutes for the flavors to come together.
Prepare the bread: Lay out the bread and add lettuce and tomato if using.
Build the sandwich: Spoon the chicken salad evenly over two slices of bread.
Finish the sandwich: Top with the remaining bread slices and gently press together.
Slice and serve: Cut each sandwich in half and serve right away.