Start by washing the cucumber thoroughly. Using a mandoline or a sharp knife, slice the cucumber into thin rounds. Place the slices on a paper towel to absorb any excess moisture.

In a small bowl, combine the softened cream cheese, mayonnaise, chopped dill, lemon juice, salt, and pepper. Mix until smooth and well combined.

Lay out the slices of bread on a clean surface. If desired, lightly butter each slice to add an extra layer of flavor. Spread a generous layer of the cream cheese mixture onto each slice of bread. Arrange the cucumber slices evenly over the cream cheese on half of the bread slices. Top with the remaining slices of bread to form sandwiches.

Using a sharp knife, carefully cut off the crusts from each sandwich. Then, cut each sandwich into quarters or smaller rectangles, depending on your preference. Arrange the sandwiches on a serving platter and garnish with additional fresh dill if desired.