Is there anyway to retain the drawing templates in LAYOUT when a license is ported over to a new computer or must they all be set up again
Yes. Just copy them over from the old computer to the new.
The default templates are in C:\ProgramData\SketchUp\SketchUp 2014\LayOut\templates
The templates you add go to C:\Users\YOUR NAME HERE\AppData\Roaming\SketchUp\SketchUp 2014\LayOut\Templates
If Anssi’s solution doesnt work for you, one can migrate each one separately by …
Open a new blank LayOut project using one of your custom templates. Immediately after the template has loaded, save it with the name of the template it represents somewhere you can find it later. After all the templates you need are saved, transfer them to a flash drive and load them onto the new installation of SketchUp/LayOut
In the new installation LayOut, File >Open each of the saved template .layout files… and File > Save as Template. This will save it in its designated template location on the harddrive and it will automatically be listed in the Template menu.