Yes. Uninstall Lightroom on your old machine and Install Lightroom on the new laptop.
Uninstalling won't delete your catalog files.
Then copy your catalog files (.lrcat, .lrdata) to your new laptop.
By default the files are located in a folder called Lightroom in your Pictures Folder.
I dont have my old mac with me, what should I do. When I enter the serial number, it says contact customer care/
I would be inclined to follow that instruction.
They will be able to help with licensing issues.