You cannot transfer the Lightroom program from your desktop to your laptop. But you can download an installer and install Lightroom on the laptop, then use your existing serial number to activate Lightroom on the laptop. Lightroom can be downloaded from the following location. Take note that the link I'm providing is NOT for the creative cloud, but for the standalone installation of Lightroom.
If you are planning on using the same images and same catalog on both the desktop and the laptop you may want to do some careful planning and ask some more questions.