Stick 1 to 2 blueberries, depending on their size, into the cavity of each lychee. Place on a foil-lined baking sheet and freeze, about 1 hour. (Wait until the "eyeballs" thaw a bit before eating, so that you don't choke on them.) Stir together 5 tablespoons of the lychee syrup, the blueberry juice and lime juice in a bowl or pitcher until combined. Stir in the sparkling water and add the lychee eyeballs. If it is a bit tart for your taste, add the remaining tablespoon syrup. Serve in tall glasses over ice, spooning the lychee eyeballs into the glasses as you pour. For a grown-up twist, stir in the gin before adding the sparkling water. Enjoy!