Combine water and sugar in a small pot. Bring to a boil and stir until sugar has dissolved.
Let cool to room temperature, add lemon juice, and transfer to ice cream maker. Follow manufacturer's instructions to make ice cream.
Remove from ice cream maker, add stir in lemon zest, and freeze for 3-4 hours.
Recipe by Things I Made Today at https://www.thingsimadetoday.com/2013/08/27/when-life-gives-you-lemons-to-make-lemon-custard-make-lemon-sorbet-instead/