Moving Local Backup drive to new computer

I have been using cloud based Lightroom and storing “local copies” on an external drive.  I just got a new Mac and was wondering if I could simply take the old external drive and plug it in to my new Mac and “select” the same folder to back up local copies going forward.  I’ve “stopped storing” local copies on the old Mac.  If so, this would prevent me from “copying over 50K phots again down from the cloud!”  Seems logical but just thought I ‘d reach out to everyone before making some huge error.