Whisk the sugar and lemon juice together in a bowl until the sugar has dissolved.
Add in the milk, heavy cream and zest and stir to combine.
Pour the mixture into a gallon sized bag and squeeze out as much air as possible when closing the bag.
Place the bag on a metal baking sheet and put it in the freezer for 4-6 hours or until frozen.
Take the sherbet out of the bag and break the slab up into pieces.
Put the pieces of frozen sherbet in a food processor and blend until smooth. Enjoy now if you prefer soft-serve! Otherwise, scoop sherbet into a metal bread pan, cover and freeze to solidify it more.