2. Beat together the egg yolks and 1/3 cup sugar until thick.
3. Warm the syrup over low heat. Whisk the egg yolks and sugar into the corn syrup and cook over low heat, whisking just until warmed through. Remove from the heat and strain through a sieve.
4. Whip the cream until it begins to mound up and peak softly, and fold it into the yolk mixture.
5. Beat the egg whites and 1 tablespoon sugar until they form soft peaks; fold into the yolk and cream mixture.
6. Stir in the melon puree and lemon juice and freeze according to the instructions for your ice cream maker.