Combine avocado and 1/4 cup half-and-half in a blender; blend until smooth. Pour mixture into a bowl, ideally one with a spout. Squeeze lemon juice over avocado mixture and stir.
Pour remaining half-and-half in the blender and shake it around to pick up any remaining avocado mixture; pour into the avocado mixture in the bowl. Add condensed milk and whisk until smooth.
Pour avocado mixture into ice cream maker and process for 25 to 30 minutes. Turn off machine and pour mixture into a 1 1/2 quart freezer-safe container; place in the freezer until ice cream is set and has increased in size, at least 3 hours.
Lime juice can be used in place of the lemon, if desired. Light whipping cream can be used in place of the half-and-half.
If using an ice cream maker with an open top such a Cuisinart®, put a towel over the top while it is mixing to hold the cold air in.
I have not tried this, but I heard that if the ingredients are cold before going into the machine, they will become ice cream faster, so you could try putting the mixing bowl in the refrigerator for a few minutes.
If your ice cream is not firm enough after three hours, overnight in the freezer will do the trick.