You required to have Internet connection and valid serial number to activate it.
Would you please let us know what exactly you are dealing with while activating it.
Please follow the below article if you are facing some specific issue mentioned in it while activation:
I installed LR6 as an update to my LR5 installtion on my Windows PC right after the purchase beginning of August. Today I wanted to install LR6 a second time (thought this is possible) on my MacBook with LR 4.4. This didnt´work since the authorization code wasn´t acceptetd. What did I do wrong?
NB: the Mac Book was connected to the internet...
I have checked your account, and you have one activation left that means you can install it on your Mac without any problem.
Please make sure you are using the right serial number.
If you still face the same problem, please send me a personal message with serial number you are using so that I can verify it at my end.