Start by washing the cucumber thoroughly. Slice it thinly into rounds and set aside.
In a medium bowl, combine the softened cream cheese, dill, lemon juice, garlic powder, salt, and black pepper. Mix until well blended and creamy.
Lay out the slices of bread on a clean surface. Spread a generous layer of the cream cheese mixture on one side of each slice.
If using, place a layer of lettuce on half of the slices. Top with cucumber slices, arranging them evenly.
Place the remaining slices of bread on top, cream cheese side down, to create sandwiches.
Cut each sandwich into quarters or halves, depending on your preference. Serve immediately or refrigerate for up to 1 hour before serving for a chilled option.