We need to grease our cider press (and other things). The off the shelf greases tend to be quite thick and pasty and everything I can think of in our kitchen is much thinner. The manufactured ones are not nearly as "food safe" as I want- containing aluminum, petrochems, etc. What would you use? I'd consider something DIY or a purchased product if it is truly safe and effective. I'm thinking cider press, meat grinder and the likes.
Historically lard would be most common. Modern coconut oil would be the vegan equivalent.
We used sunflower oil for ours as there was less chance of imparting flavour to the cider. We just needed the oil to get started and to protect the metal in storage as the apple juice gets everywhere and behaves like a lubricant.
There are mineral oils that are officially foodsafe, but we didn't try these.
Having it appropriately greased for storage is very important but greasing to use it is going to help decrease the muscle power needed every time we raise and lower the press too so I'm looking for something to use all around. Work smart, not hard! Lard sounds like a good solution. I know "they" say mineral oil is food safe, but they say the same about the other wacky petrochemical products too. We're more cautious than that.