Google is your friend. From http://labs.adobe.com/technologies/eula/lightroom.html
2.4 Portable or Home Computer Use. The primary user of the Computer on which the Software is installed may install a second copy of the Software for his or her exclusive use on either a portable Computer or a Computer located at his or her home, provided the Software on the portable or home Computer is not used at the same time as the Software on the primary Computer.
That means what you want to do would be outside the terms of the Adobe licence. As far as I'm aware, Adobe doesn't check whether the second copy is for the exclusive use of the primary user, and not used at the same time as the copy on the primary computer.