Nikon D4 has a Nikon F lens mount and currently there are 287 native lenses available for this mount.
Nikon D4 doesn't have a sensor based image stabilization system but 55 of these lenses already comes with optical image stabilization.
Since Nikon D4 has a Full frame sensor, it has a focal length multiplier of 1× so lenses will provide their original focal length on D4.
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Nikon D4 Lenses with Image Stabilization
Nikon D4 Lenses with Weather Sealings