One Lightroom license entitles you to two separate installations, Windows or Mac or both. But the two installations are for your personal use. In other words, to satisfiy the terms of the license only one of those installations can be in use at any given time.
I have the same question on Lightroom 4.4 and assume the answer is the same. The next question is, how do I do the installation on my laptop. I haven't found instructions on the Adobe site.
how do I do the installation on my laptop.
Same way you did the installation on your other computer