If you cannot start Lightroom CC 2015 (not sure about 6 standalone) and the trick with signing out and back in doesn't work, you could try this solution, based on "Just downloaded Adobe Lightroom 6 trial version, but app won't open on my mac? - Fuji X Post Processing - Fuji X Forum":
If you also have 5.7.1 installed through CC it now won't open the develop module. To re-enable Lr 5 restore the original .lic file. Looks like due to some mishap both versions cannot be activated at the same time (I don't think it was intended).
Thank you. Works fine now.