Place the cooked chicken in a large mixing bowl and shred it into small, even pieces for better texture.

Add mayonnaise, mustard, salt, and black pepper to the chicken. Mix slowly until all the chicken pieces are evenly coated with the creamy dressing.

Continue mixing until the mixture becomes smooth, creamy, and consistent with no dry spots visible.

Add the finely chopped celery and onion. Stir gently to distribute them evenly throughout the mixture.

Taste the mixture and adjust seasoning if needed. Add a small amount of lemon juice if you want a fresher flavor.

Lay the bread slices flat on a clean surface. Toast lightly if desired for a firmer base.

Spread an even layer of the chicken mixture onto one slice of bread, making sure to cover the surface without overfilling.

Add lettuce leaves and tomato slices on top of the chicken mixture for freshness and texture.

Place another slice of bread on top and press gently to hold the sandwich together.

Cut the sandwich into halves and serve immediately, or chill briefly before serving for best results.