From your old laptop please make sure you have sign out from Lightroom 6 and deactivate Photoshop elements 10.
The option to sign out and deactivate in both the application would be under Help menu.
After this you can uninstall it from the computer and can install and activate on new computer.
For more information please check the following Learn to activate or deactivate Adobe apps.
P.S. If you do not see an option to sign out or deactivate in Photoshop elements then simply uninstall it.
Links to download:
Lightroom 6: Download Photoshop Lightroom
Photoshop Elements: Download Photoshop Elements | 14, 13, 12, 11, 10