You do have to register the software when the license code is input. I believe, if there is more than the permitted number of installations under the same license number (2) Adobe will not permit the additional install.
But, there may be issues if you try to install the software with the same license on computers with different operating systems.
At the end of the day, Lightroom isn't that expensive. If your daughter is in school she may be able to get an educational discount, making it even less expensive. Just get her a legitimate copy.