Drain the lychee syrup into a small pan. Cut the lemongrass into thirds and bruise with the back of a chef's knife. Add the lemongrass to the lychee syrup and bring to a boil over medium-high heat. Reduce the heat and simmer for 2 minutes. Remove from the heat and cool to room temperature. Strain and store in the refrigerator until ready to use.
Puree the lychees in a blender or food processor. Add the strained lemongrass-lychee syrup and blend a few seconds more.
Fill one-third of a Champagne flute with the puree mixture and top off with Champagne. Garnish with a small strawberry.