I have a vintage Whizzer J engine and I mean the pulley that moves when you pull on clutch.
First i don't mix oil with the gas and second the flywheel is not in contact with any parts of the engine that has oil. It looks like a sealed bearing to me
The bearing in the clutch pulley is a shielded roller bearing. If it is dry/loose/noisy, press it out, throw it away and install a new one. If you are on a really tight budget (they cost ~ $10) you could pry the shield off, clean it, regrease, and attempt to replace the shield. But why?