Basically, Li-Air elements are wasting the energy from the phase change of oxygen. When a Li-Ion battery is discharged, you get the gaseous oxygen and bind it into a solid state molecule.

To do that, you need to expend roughly the same amount of energy that is needed to first liquify and then solidify the oxygen.

In fancy chemistry-speak it's called "entropic loss". You do gain some of that energy back when the battery is charged, as oxygen goes from a well-ordered solid state into the gaseous state. But it's not 100%.