Combine the cream cheese, dill, lemon juice, lemon zest, salt, and pepper in a bowl. Mix to combine thoroughly.
To make open-faced sandwiches: Trim the crusts from the bread slices. Spread the slices with the cream cheese mixture. Cut the bread slices in half diagonally to form triangles. Shingle cucumber slices on top. Serve.
To make closed sandwiches: Spread slices of bread with the cream cheese mixture. Layer cucumber slices on half of the bread slices. Top with the remaining bread slices, cream cheese side down. Trim the crusts off the sandwiches. Cut into triangles or rectangles and serve.