Your Lightroom License is a single user/ owner. It is a cross platform license PC and or Mac.
You can have two installations current with one in use at any point in time.
There is no deactivate process so you can uninstall and install as many times that it is necessary.
Mac update downloads are available at the link below.
Download the latest update of the LR version you own, install and input the license.
Info is available for making the move here.