How to Make It
Place wine, sugar, lemon zest, and thyme in a large saucepan. Bring to a boil over medium-high; boil, stirring occasionally, until sugar dissolves, about 5 minutes. Remove from heat; set aside at room temperature to cool completely, about 30 minutes. Cover and chill 8 hours or overnight.
Scoop 20 balls out of each of the cantaloupe and honeydew halves using a melon baller. (Discard remaining fruit, or reserve for another use.) Pour chilled wine mixture through a fine wire-mesh strainer into a medium saucepan. Bring to a boil over high; reduce heat to medium, and simmer until reduced by half, about 5 minutes. Add melon balls to saucepan, and remove from heat; set aside at room temperature to cool completely, about 30 minutes.
Stir basil into cooled melon mixture. Divide melon balls and sauce evenly among 4 serving bowls. Top each bowl with a scoop of lemon sorbet, and serve immediately.