Is it possible to make salty avocado Ice Cream without a machine? I'm trying to make salty avocado ice cream for a culinary school project, but don't really know if it's possible. 

I've found several no-churn recipes, but most of them use sweetened condensed milk. I'm trying not to use any sweeteners (or as few as possible), as this will be a cold entrée. 

Would it be possible to have some sort of mix made of processed avocados, some heavy cream, lemon and a bit of salt/pepper (resembling a simple guacamole) and have this turned into ice cream?

I've thought about using dry ice for it but not sure if it would work. I might also be able to use a KitchenAid ice cream maker attachment.
On the question of dry ice, yes...it makes excellent ice cream using a kitchen aid and the beater in the standard bowl.  It is best if you pulverize the dry ice in a blender first.  You will want to avoid using too much (your base will become carbonated, but you can allow it to off-gas). Add a little at a time until the appropriate texture is achieved. Make sure it is not possible for someone to eat a chunk of dry ice!