follow the directions above, however you will need to remove /dev/mapper before mkdir /dev/mapper (as /dev/mapper is actually a link to the live-cd and therefore read-only).
rm -Rf /dev/mapper
mkdir /dev/mapper
and continue with the rest of the instructions....

Personally I think it should be part of knoppix and not require such dramatics. Dev-mapper is already included and should be copied over to /etc instead of linked, then they could install lvm2 and run it on both kernels. It is a small program and would be trivial to implement.