Leica CL has a Leica L lens mount and currently there are 146 native lenses available for this mount.
The latest released lenses that are compatible with the CL are the SG-image AF 35mm f2.2, the 7Artisans 135mm f1.8 L and the TTArtisan 50mm f1.8 NEO L.
Leica CL doesn't have a sensor based image stabilization system but
18 of these lenses already comes with optical image stabilization.
Since Leica CL has a APS-C sensor, it has a focal length multiplier of 1.5x 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 CL.
You may also also be interested in these:
Leica CL Lenses with Image Stabilization
Leica CL Lenses with Weather Sealings