Put the lychee fruit in a large bowl and mash it (you can use a potato masher or cocktail muddler) until it is finely pureed.
Pour the mashed lychee through a strainer (fine-mesh) over a bowl to remove the solids from the liquid, pressing the fruit pulp to ensure you have extracted all of the fluid.
Place the lychee fruit puree into a jar or other glass container that has a lid and refrigerate until ready to use. Don’t keep the lychee puree for any longer than 1 to 2 weeks.
Or you can freeze the puree with small portions or in forms of ice cubes. What about the pulp left: eat them.