It has been awhile since I worked on one of these, but most Canon LTM lenses can be taken apart by removing the lock ring aound the rear element, which allows the entire lens group to be pulled out of the focusing mount. There may be two lock rings around the rear element, remove the outer one.
Once the lens assembly is removed from the helicoid, you can usually unthread the rear group from the front group, allowing you to clean both. Be careful not to lose any spacers which might be between the lens assembly and focusing helicoid.