1. Remove 4 lychees from the can and skewer on decorative toothpicks/cocktail skewers, 2 per skewer. Place on a small baking sheet or plate and place in the freezer until frozen firm. Reserve for garnish.
2. Combine the sugar and water in a small saucepan and bring to a simmer. Cook for a minute or so or until the sugar is dissolved. Pour the syrup into a blender along with the remaining lychees and the lychee syrup. Zest and juice the lemons into the mixture and then puree until completely smooth. Pour the mixture through a fine-mesh strainer and discard the solids. Refrigerate the lemon lychee syrup until cold.
3. When ready to serve, combine the vodka, lychee liqueur, Cointreau, and ¼ cup of the lemon lychee syrup in a shaker filled with ice. Shake vigorously until well chilled and then pour into chilled martini glasses. Garnish with the skewered lychees and lemon twists and serve.

Note:

1. If you can’t find this liqueur, you can skip it and increase the lychee lemon syrup by another ¼ cup.