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

Using a sharp knife or a mandoline, thinly slice the cucumber. Peel the cucumber if the skin is tough and pat the slices dry with a paper towel to remove excess moisture.

Spread a thin layer of butter on one side of each bread slice. Spread a generous layer of the cream cheese mixture on the buttered side of four bread slices. Arrange the cucumber slices evenly over the cream cheese, then top with the remaining bread slices, buttered side down.

Using a sharp knife, trim the crusts off the sandwiches for a more elegant presentation. Cut each sandwich into quarters or smaller rectangles and serve immediately.