Whisk together the sugar, lemon juice, and limoncello in a bowl until the sugar dissolves. Heat in the microwave for one minute to speed this up. Add the zest of one lemon.
Add the milk and heavy cream and stir to combine.
Pour the mixture into a gallon sized zip lock bag. Squeeze out as much air as possible when closing the bag.
Place the bag on a metal sheet or metal baking pan and put it in the freezer for 4 to 6 hours or until frozen.
Take the sherbet out of the bag and break the slab into pieces.
Put the pieces of frozen sherbet in a food processor and blend until smooth; 3 to 4 minutes.
Eat it right away for a very soft sherbet or place in a metal bowl, return to the freezer and freeze to solidify further.