Drain lychees in a colander over a bowl; reserve 1 cup syrup. Discard remaining liquid. Drop 1 lychee in the bottom of each of 5 glasses; fill each glass halfway with crushed ice. Reserve remaining lychees for another use.
Combine reserved 1 cup lychee syrup, juice, and vodka in a large martini shaker filled halfway with ice; shake until well chilled. Strain 1/2 cup syrup mixture into each prepared glass; garnish each serving with 1 grapefruit section. Serve immediately.