500 ml (2 cups) simple syrup (made up of equal parts water and sugar; stir until dissolved; bring to boil, take off from heat; let cool. Alternatively, simply mix water and sugar together and shake vigorously until the sugar has dissolved)
250 ml (1 cup) water
(optional) 1-2 tablespoons of gin or vodka (will make the sorbet softer, to the prize of adding to the time it will take for the sorbet to freeze sufficiently. This is usually not a problem if you have an ice cream machine but may be a factor when still-freezing, using the household freezer).
(optional) 1 egg white, lightly whipped OR about 100-150 ml Italian meringue or Aquafaba
Instructions
Make the simple sugar syrup (see above). Let cool down.
Grate and, if necessary, fine-chop the zest.
Combine the juice, zest, simple syrup, and water.
If using, add the gin or vodka.
Churn in your ice cream machine according to instructions, possibly adding a lightly whipped egg white to the sorbet base for improved texture and consistency (usually not necessary if the sorbet is likely to be consumed very soon after being finished).
Still-freezing (without using an ice cream machine):
Refrigerate the sorbet base until chilled. Put in a (preferably rather flat) freezer-safe container, cover with plastic film and lid, and put in the freezer. After about 45 minutes, take out and churn the sorbet with a fork or similar, evening out what has started to freeze and breaking (too) large ice crystals in the process. Return the sorbet to the freezer and then repeat the churning every 45 minutes or so for at least 3-4 hours.
You could also gently whip up and add 1 egg white to the sorbet once it has started to gain some consistency (like after 1-2 hours in the freezer) - that will also make the final sorbet "lighter/softer" and improve the consistency.
Recipe by ICE CREAM NATION at https://www.icecreamnation.org/2012/05/lime-sorbet/