Sorry, can't help with that question (1) I don't have a Mac and (2) I don't use Lightroom
But I would make a separate backup of the LR catalog and the Previews folder to some other media, like another external drive, and Restore those back to the external drive you plan on using.
I don't trust Time Machine to do this.
Also it is a very bad idea to use the same external drive for TM backups and storage of other files. TM should have its own dedicated external drive.