I have upgraded to LRT 5.02, (uninstalling LRT 5.0 & 4.0 prior as instructions). 
Am now being requested to 'Activate License Key'! 
First time ever asked this having been original user since LRT 1.  I also upgraded to LR 6.14.
How do I recover my License Key?

You just recently upgraded to LRTimelapse 5 and therefore got a new license key via Email that you installed. Just do the same again, if LRTimelapse is telling you to. Get the license key from that email and install it again.
If you want me to resend it, please contact me via support(at)lrtimelapse(dot)com