Adobe recommends not to use TM while LR is running.
Is this still a Problem and what is happening if u do it?
Im running LR on a separate HD wich is not included in the TM-Backup, but i write the Kataloge Backup on the Mac-HD witch is backed up by TM. Is this a possible workaround?
I don't think your solution is a good one. The reason Lightroom should be closed is so that that catalog is in a stable and unchangeable condition at the time of the backup. If the catalog is open and you are making changes that are being written there is a possibility of file corruption, or a possibility that changes you are making won't get written to the TM backup.
Adobe still recommends in their Help not to rely on Time Machine backups of the catalog made while LR is running.
However, I think your approach is OK. The catalog backups made by LR land on a hard drive that is backed up by Time Machine. Those catalog backups are never changed once written by LR, and thus Time Machine will do an adequate job of backing them up.