Juice fresh lemons to obtain the required lemon juice. Finely chop fresh basil leaves and set aside.

In a saucepan, combine equal parts of water and sugar over medium heat, stirring until dissolved (3-5 minutes). Remove from heat and let cool.

Pour lemon juice and chopped basil into cooled syrup, stirring well to combine.

Cover and chill the mixture in the refrigerator for at least 4 hours.

Pour the chilled mixture into an ice cream maker and churn according to the manufacturer's instructions (20-25 minutes).

Transfer churned sorbet into an airtight container, smoothing the top. Freeze for a few hours until firm.