3-jaw chuck grease sounds like something that would probably be a mixture of 1-part bear grease, 2 parts snake oil, and 1 part Mother Fletcher's geese grease. Also not to be confused with or mixed with 4-jaw chuck grease...........
Not exactly your question ....but I disagree with the statement "never use grease on a 3 jaw chuck".
That is not true if it is a SMW chuck....however....I am unaware of them making a manual chuck. The grease in a SMW chuck has some hydraulic properties as well. If something other than the correct grease is used you find that you lose grip force and can have concentricity / repeatability issues. And if over greased you can crack them or deform the face.
This has been a really good read, thx guys. FYI, I used super clean to soak my whole chuck in after I took it apart. After letting it soak for two days all of the dried and hardened grease wiped right off. I have a 1919 Hendey Lathe that I am restoring. I share my content on YouTube if you are interested in a one arm guy doing dumb two arm things lol, my channel link is below. Thx again for this thread. I am new to owning a lathe so I am learning a lot.