Panasonic BGH1 has a Micro Four Thirds lens mount and currently there are 132 native lenses available for this mount.
The latest released lenses that are compatible with the BGH1 are the Brightin Star 60mm f2.8 II, the 7Artisans 50mm f1.2 APS-C and the Pergear 50mm F1.2 APS-C.
Panasonic BGH1 doesn't have a sensor based image stabilization system but
39 of these lenses already comes with optical image stabilization.
Since Panasonic BGH1 has a Four Thirds sensor, it has a focal length multiplier of 2× 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 BGH1.
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Panasonic BGH1 Lenses with Image Stabilization
Panasonic BGH1 Lenses with Weather Sealings