Peel and pit the avocados. Add the avocados, lemon juice, milk, and sugar to a blender and puree. Transfer the mixture to a medium mixing bowl, add the heavy cream and whisk to combine. Place the mixture into the refrigerator and chill until it reaches 40 degrees F or below, approximately 4 to 6 hours.
Process the mixture in an ice cream maker according to manufacturer's directions. However, this mixture sets up very fast, so count on it taking only 5 to 10 minutes to process. For soft ice cream, serve immediately. If desired, place in freezer for 3 to 4 hours for firmer texture.