You have to own Cubase LE license. LE is an OEM license, so you can get it only with hardware. Some hardware vendors are bundling Cubase with their hardware. This is the only one way, how to get it. You cannot buy. If you want to buy the lowest Cubase license, there is Cubase Elements.
In any case, you will need 2 licenses (Cubase Pro, and Cubase LE or Elements).
The other question is, if you will be able to edit Cubase Pro project in Cubase LE/Elements. Yes, you can open the project and you can work on it. But be aware, Cubase LE/Elements is limited. So for example if you reach the track count limit, you will see and here the other tracks, but you will not be able to edit them. Some features are missing, so if you are using these features in Cubase Pro, you will not get them in LE.
Why you don’t take your USB-eLicenser with you and why you don’t use Cubase Pro on the other machine? This is totally legal. You can install Cubase to many computers. Then you can start it on the computer, where do you plug your USB-eLicenser in.