In a small saucepan, combine the water, sugar, lemon zest and lemon juice. Bring to a simmer and cook until the sugar is dissolved, about 10 minutes. Add the basil and mint and set aside to steep for 3 minutes. Strain syrup through a fine mesh sieve and set aside to cool. Transfer to the refrigerator until thoroughly chilled, then process in an ice cream machine according to manufacturer's directions. Transfer to a freezer-proof container with a lid and freeze until ready to serve.
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