Currently there are 15 native Standard Zoom lenses for Olympus E-M5 III and all of these lenses are autofocus (AF) type.
E-M5 Mark III also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on E-M5 Mark III.
Since Olympus E-M5 III has environmental sealings (Weather Sealing), you may like to couple your camera with one of these 6 Standard Zoom lenses with Weather Sealings.