Cut the cucumber into rounds that are about 1/4 inch thick.
In a mixing bowl, beat the softened cream cheese, dill, lemon juice, salt, and pepper until it's well combined and creamy.
Using a small spoon, put a dollop of the cream cheese mixture on each cucumber slice.
Top each cucumber slice with a piece of smoked salmon.
Sprinkle with additional fresh dill, salt, and pepper to taste.
Arrange the cucumber bites on a serving platter.
Chill in the refrigerator for 10-15 minutes before serving.