The lube needs for O/U are not that demanding. It is not like we are moving 11,500 rpm crankshaft speed, or operating in salt water. I found Lubriplate in small toothpaste tubes. It is convenient and I have no wear issues.
Grease is pretty much oil plus soap to thicken it, so not much of a difference except how thick it is. Both oil and grease provide lubrication, but grease sticks around longer and picks up more soil.
I think we spend too much time and money on special stuff, when a quart of a high-quality motor oil almost always does the trick in a gun that is cleaned regularly. Soak small parts in a jar of 10W-40 and wipe off all you are able to reach. If I shot 1,000 rounds on a Saturday I might change my tune, but I don't.
I have been using the krieghoff grease lightly. Cant see it but feel there's a film on it. Debris has caused it to scratch it and then it was suggested to use mineral spirits to clean it up and look like new again.
The same person said they had the oil penetrate the stock and if he continued would have caused issues.