The term “catalog” in reference to LR is the database with all the settings and photo locations in it. It does not mean the photos, themselves. Since you ask about sharing a catalog on two computers are you really asking about also sharing the photos, too, or are those somewhere that can be accessed by both computers, already?
I have two PCs I work with my photos on and have everything on an external hard-drive that I can plug into either computer.
LR is not really designed to work on photos and catalogs on two different computers, unless, as in my case, the photos and catalog are stored on an external device that can be moved between them.
Because all my photos are on an external drive that can easily be dropped or lost or stolen, I always make a copy of my changes to another external drive that I don’t move between the two computers using a hard-drive replication utility.
If you are going to be travelling then I’d have a backup of the photos and catalog on more than one external drive that you travel with but store in another location in your luggage or hotel-room/locker so you don’t lose both at the same time, and probably another copy back home so you don’t lose everything even if there is a catastrophic accident on your trip.
Thank you for your response. I currently have my master catalog and originals on an external hd. I bu to another external hd. I now have a desktop in my studio that I'd like to work primarily from, but because I travel and sometimes like to work from my sofa, I want to be able to work from my laptop as well. So, I guess my question is, can I put the catalog on the new device, while keeping it on the external hd that I've been using all along and be able to keep everything synced? If so, how the heck do I accomplish that?
I would just keep the catalog and originals on the external drive... simple.