1.In a medium bowl, combine vodka, juice, sugar and mint.
2.Pierce melon flesh several times. Puncture outer skin. Strain vodka mixture into jug; pour half of it, gradually, over melon flesh. Enclose melon halves separately in plastic wrap; freeze overnight.
3.Remove melon from freezer; stand at room temperature 1 hour. Remove skin; chop melon coarsely.
4.Blend or process melon with remaining vodka mixture, in batches; pour each batch into punch bowl. Stir in lemonade.
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