Preparation Heat sugar and water in a 1-quart saucepan over high heat, stirring, until sugar is dissolved, then pour into a heatproof bowl set in a large bowl of ice and cold water. Let stand, stirring occasionally, until syrup is cold, about 3 minutes. Purée lychees with sugar syrup and lemon juice in a blender until smooth, then force through a fine-mesh sieve into a bowl, pressing hard on solids and then discarding them. Fill cocktail shaker halfway with ice cubes and add lychee purée, vodka, and Cointreau. Shake 15 seconds and strain into Martini glasses.
Preparation Heat sugar and water in a 1-quart saucepan over high heat, stirring, until sugar is dissolved, then pour into a heatproof bowl set in a large bowl of ice and cold water. Let stand, stirring occasionally, until syrup is cold, about 3 minutes. Purée lychees with sugar syrup and lemon juice in a blender until smooth, then force through a fine-mesh sieve into a bowl, pressing hard on solids and then discarding them. Fill cocktail shaker halfway with ice cubes and add lychee purée, vodka, and Cointreau. Shake 15 seconds and strain into Martini glasses.