Halve the avocados, remove pits, and use a large spoon to scoop out the flesh.
Place avocado, lemon juice, milk, and sugar in blender carafe and puree until smooth.
Reduce blender speed to low and slowly add the cream.
Chill the mixture in an air-tight container until it reaches 40°F or below, 4 to 6 hours.
Process the mixture in an ice cream maker according to the manufacturer's directions. This mixture sets up very fast, so count on it taking only 5 to 10 minutes to process to soft-serve consistency.
Serve immediately or harden in freezer for 3 to 4 hours for a firmer texture.