There may be a recommendation from one of the cylinder-mower manufacturers on that. The issue is that oil or grease is great if it is clean, but if it gets dirt in it, it acts as a cutting agent and wears the parts worse than running unlubricated would. So, if experience shows that dirt doesn't get in there, you would lubricate with something like water pump grease, that is so stiff it does not circulate (which would move any dirt that did get in, across the full width of each bearing surface).
