Nikon D4 has a Nikon F lens mount and currently there are 257 native lenses available for this mount.
Nikon D4 doesn't have a sensor based image stabilization system but 53 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.
You may also also be interested in these:
Nikon D4 Lenses with Image Stabilization
Nikon D4 Lenses with Weather Sealings