The question I received was whether multiple users can share in Lightroom. The direct answer to the question is no, Lightroom isn't designed for multi-user access across a network.
On the other hand, many of us use a form of "networking" with our personal systems. In other words, I access the same images from my laptop and desktop systems. Remember, the photo files you have Lightroom point to aren't stored in the Lightroom database (catalog) file. They're pointed to by the catalog. It's not uncommon for photographers to have a central (or even remote) drive on the network where all images live. Indeed, I'd recommend it, otherwise your backup chores will get very complex very fast. My images live on a dedicated data drive that can be reached by both my machines. Lightroom points to those images no matter which computer I use. For example, I have one catalog file, which I synchronize between the laptop and desktop using Chronosync (Mac program). I just have to make sure that I never have the catalog open on both machines at once making changes.