Leica Digilux 3 has a Four Thirds lens mount and currently there are 47 native lenses available for this mount.
The latest released lenses that are compatible with the Digilux 3 are the Venus 33mm F0.95 CF APO, the Samyang 135mm F2.0 ED UMC and the Samyang 300mm f6.3.
Leica Digilux 3 doesn't have a sensor based image stabilization system but
3 of these lenses already comes with optical image stabilization.
Since Leica Digilux 3 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 Digilux 3.
You may also also be interested in these:
Leica Digilux 3 Lenses with Image Stabilization
Leica Digilux 3 Lenses with Weather Sealings