How do you have your Lightroom set up that requires you to have Wi-Fi?
They both stopped working at the same time. If they're seperate issues what's the problem with Lightroom? I've checked again. It opens then I get a message saying "not responding" when I try to move to a different folder, or move from library to develop, or do some editing. It's really slow. It'll do a bit but won't let me compare photos at all.
I'm using Lightroom CC. Have never had Lightroom 6. But it's my understanding that once you are set up you don't need an Internet connection. Try signing out from the application manager and see if that helps. If not, maybe someone with Lightroom 6 can shed some light.