These little engines run at a high rpm with the compression created by a seal between the piston itself and cylinder wall. Any amount of dust breathed in will cause permanent damage to the engine and shorten it's life.
I wouldn't run one with a dry filter. You can risk it and use some other...
Odds are, bicycle chain lube isn't a good choice. For RC filters, you want sticky air filter oil. I've used motorcycle oil for years on mine, PJ1:
https://www.rockymountainatvmc.com/parts/pj1-foam-air-filter-oil-p
I soak the filter with wd-40, work it through to clean it. Then use dish...