LR 4 deactivation?
Unlike Photoshop (which does have and require activation) so is very tightly controlled by Adobe - try to load a adobe serial into a 3rd computer and when it tries to activate, Adobe very politely tells you that you already are using your 2 activations, and one needs to be deactivated before you can add your "3rd" computer.
Lightroom, since version 1 is more of an honor system, you have a serial number, but there is NO activation. So, you could run it on 3 (or more computers) and Adobe would never know.
The short answer to your original question is just uninstall the program to give more hard disk space (I'm pretty sure that things like backups which can be sizable, especially if you don't prune them once in a while) do not get removed) so you will need to manually remove those after uninstalling the program to maximize the free hard drive space for your mother-in-laws new computer.
Thank you for the info!