How do I remove Photoshop CC 2015 & Lightroom from one computer and install on a new computer?

Hi,

On the Old machine you'll have to first sign out to deactivate the subscription from that ma chine and then uninstall the apps if you no longer wish to use the apps again on that machine.

Please see the below links fro the same :

Sign in and sign out to activate Creative Cloud apps

Uninstall or remove Adobe Creative Cloud apps

On your new machine use the following link to install Creative Cloud app on new machine : Download Adobe Creative Cloud apps | Free Adobe CC trial

Also see,

Download and install Adobe Creative Cloud apps

Let us know if this helps.

Regards,

Bani