Puree half of the lychees and all of the syrup in a blender until all lychees are liquefied. Strain through a fine mesh strainer, pressing down to get the most from the lychees into a clean pitcher; discard the fibrous solids. Add the Lillet, rosewater and bitters. Refrigerate to chill thoroughly, if needed.
Pour into chilled flutes, martini, or fun juice glasses, and garnish with an orange twist or slice. Drink.