Leica CL has a Leica TL lens mount and currently there are 66 native lenses available for this mount.
The latest released lenses that are compatible with the CL are the Sigma 14mm F1.4 DG DN, the Sigma 23mm F1.4 DC DN C and the Sigma 17mm F4 DG DN C.
Leica CL doesn't have a sensor based image stabilization system but 10 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