Download & Install instructions https://forums.adobe.com/thread/2003339
-kglad links in reply #1 here https://forums.adobe.com/thread/2260248 will help
-you will need to enter your original serial number during install for non-Cloud programs
-download Lightroom https://helpx.adobe.com/lightroom/kb/lightroom-downloads.html
-Cloud Getting Started https://helpx.adobe.com/creative-cloud.html
-Membership questions and problems https://forums.adobe.com/thread/1146459
Is this a perpetual or a subscription license?
If I understand well, since you didn't install it yet on the old laptop there was no activation? Did you try to install on the new laptop. You can install the license on two systems, provided you don't use them at the same time. Of course, best would be to deactivate on the old system, if it was activated. I cannot help you with that, you have to contact Adobe, I'm just a user.