I would advise to clean it first, I normally use a clean paintbrush and the hose of the vaccuum cleaner. Lint+oil will create a sticky sludge, and canned air will blow crap further into the mechanics instead.
what make and model is your machine? (edit: nvm I missed the link in the OP, what a neat machine!)
after cleaning and oiling (just drops, wipe of excess), does it turns smoothly if you crank it by hand, or are there any noises?
doesn’t need to be a fresh vat of milkshake every time… just reuse until no longer liquid