how does the lifetime air filter work?

The negative side to a "lifetime" filter is the element is OIL coated, there cleaned with spray or simply re-oiled BUT, on modern vehicles which use a MAF sensor that meters grams of air into the engine, OIL isn't a good thing and it's only a matter of time until oil makes it to the MAF. IF you clean the MAF frequently fine...use an oiled filter otherwise filters are inexpensive and easy to change. THIS pertains more to performance or people seeking high fuel economy, than low or no maintenance filters.

Lifetime oiled filters cause more issues than they help. Regular filters are cheap and filter better.