Make ginger simple syrup by combining ginger, and 1 cup water and 1 cup sugar in a small saucepan and simmer until sugar has dissolved. Set aside to cool. Peel cucumbers and cut half of 1 into thin slices. Puree the remaining 1 1/2 cucumbers in a blender. In a shaker, combine sake, pureed cucumber, ginger simple syrup and lychee juice. Shake to combine and serve in ice filled glasses garnished with lychee fruit.