Why does the air filter on a lawn mower need to be oiled?
Is it true that major engine damage will occur if the intake air filter is not oiled?
Specifically a foam filter for a lawn mower needs oiled, but just lightly. A foam filter lacks the ability to stop small particles as compared to a paper filter. The oil is added to make the filter "sticky" to these small particles giving the foam filter better filtering capability.
As far as major engine damage, probably not. Worst case scenario the engine wears out faster then normal due to friction caused by the particle size that is allowed through.