Puree melon, 1/4 cup sugar, 1 tablespoonlemon juice, and pinch of salt in blender;pour into 8-inch square pan. Freeze 1 hour;whisk. Freeze until solid, 3 hours. With fork,scrape into icy flakes. Cover; keep frozen.
Stir 1/2 cup sugar, 2 tablespoons lemonjuice, and ginger in pan over low heat untilsugar melts; cool.