This may not work, and may cause all kinds of problems. Use at your own risk.
I have all of my image files located on a NAS. I access this NAS using a variety of computers, but most importantly, my "office PC" (where I do all of my editing) and my living-room PC (where I occasionally like to browse my LR catalog, but never edit anything).
Here is the problem: Lightroom will happily read image files from a NAS, but refuse to open a catalog from my NAS ("Lightroom Catalogs can not be opened on network volumes, removable storage, or read only volumes". I have a proposed solution:
Computer A (the editing computer) has a local .lrcat that it reads and write to. It is setup to backup that catalog every week to my NAS.
Computer B (the living room computer) will on every lightroom startup copy the latest lrcat backup found on the NAS into a local folder, and work against it.
Practically, computer B use a batch file that does the magic (inspired by http://stackoverflow.com/questions/97371/how-do-i-write-a-windows-batch-script-to-copy-the-newest-file-from-a-directory
SET LRExePath="C:\Program Files\Adobe\Adobe Photoshop Lightroom 4.4\lightroom.exe"
FOR /F "delims=|" %%I IN ('DIR /S "%LRCatSourcePath%\*.lrcat" /B /O:D') DO SET NewestFile=%%I
copy "%NewestFile%" %LRCatDestPath%
I call this file with a desktop shortcut that lends the Lightroom icon and with the Run property set to "Minimized" to avoid the command-line pop-up. Thus with a single click I can launch Lightroom with a catalog that is (at most) 1 week old.