Panasonic GH4 has a Micro Four Thirds lens mount and currently there are 125 native lenses available for this mount.
The latest released lenses that are compatible with the GH4 are the Rokinon 7.5mm f3.5 Fisheye, the Samyang 7.5mm F3.5 Fisheye MFT and the OM SYSTEM 9-18mm f4.0-5.6 II.
Panasonic GH4 doesn't have a sensor based image stabilization system but
37 of these lenses already comes with optical image stabilization.
Since Panasonic GH4 has a Four Thirds sensor, it has a focal length multiplier of 2x so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on GH4.
You may also also be interested in these:
Panasonic GH4 Lenses with Image Stabilization
Panasonic GH4 Lenses with Weather Sealings