I've tried cleaning lightning connectors in the past, and while I've gotten them to physically look okay, they NEVER work again.
Right now my case charges fine if it's plugged in to power by itself (with the phone removed), but the phone's connection-seeing the case, connecting cleanly to my PC, charging from the case, is all hit and miss, even after multiple reboots and re-connections. Wondering if there's a way to clean it safely or fix it period. Well, it's getting worse now, and the physical connector in the case is turning partially green (despite being physically connected to the phone 100% of the time). Off and on I've had issues with it, but they've been solved by rebooting and connecting/disconnecting the case and phone until they both work.
I bought a Smart Battery Case with my iPhone 6s last year, hoping that by having the phone permanently plugged in to the case, it would protect the lightning connection. So far I've had 100% of lightning connector devices fail (never had an issue with the dock connector nor USB). This site's probably more useful anyway though :-D Tried posting on and for some reason it's not letting me.