In a food processor, grind the lemon verbena leaves and sugar together in a food processor until the mixture turns into a bright green paste, about 30 seconds. Stop to scrape down the sides as necessary. Add the lemon juice and process for 15 seconds longer, then add the water. Strain the resulting liquid through a fine sieve to remove any bits of leaf. Freeze in an ice-cream maker according to the manufacturer's direction.
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