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.
Recipe courtesy Emeril Lagasse, Emeril's Food of Love Productions, 2007