Final Cut Library Manager analyses large quantities of data for each library. Based on the media, library and network protocols, as well as the network infrastructure, this may take time.
We have tested as many different workflows as we can, and the software had been subjected to many optimisations. Nevertheless, we can't guaranty perfect fludity when using network volumes.
For this reason, we ask to try the free version of Final Cut Library Manager to ensure that it meets your needs before you purchase.
In addition, we suggest that you follow Apple's recommendations in the article Use shared storage with FCP.
This won't fix the slowness explained above, but it might improve them a bit.
How to try to improve the speed of the application
In case the performance isn't related to your network environment, you can try reinitialising Final Cut Library Manager's database:Back Reinitialising the database...