This is a refreshing dessert; serve from 6 to 12; vary the size of the scoop and garnish with a mint leaf. Use any orange-flesh melon; about 4 lbs will yield 5 cups cubed).
Peel and seed melon and cut into chunks. Puree melon with sugar, honey and lemon juice in a food processor.
Freeze in an ice-cream maker as usual; about 20 to 30 minutes. Or: simply place the mixture in a shallow metal pan and freeze until firm. Transfer to a food processor and process until smooth and fluffy. Serve immediately, or return to the freezer until serving time. For the best flavor, ices should be served within 2 to 3 days. Use waxed paper or saran wrap prevent the top from drying during storage.