since problem reappeared again, I had to try something different.
First I have to say that I got LG G2 D801 (T Mobile), but it is used outside US with an international sim card. Even though I tried all above mentioned options, problems came back again, that is, ghostly movement of screen, and double knock not working.
I read that problem with ghostly movement is addressed to digitizer being damaged, I can assure you it is software problem only.
Steps that I took to pinpoint the problem.
1. As soon as I removed sim card from the phone, everything was working perfectly, super respond and all.
so, I thought maybe my sim card its the cause, but
for long time I suspected that T mobile applications might be the cause of what was happening to my phone lately, so I decided to root it so I can install an application for removing preinstalled application, in this case T Mobile applications. Once removed, I turned my sim card back and everything started to work perfectly. Phone is responding like it was a brand new phone.
So, in my case, problem was caused by T-Mobile applications.
So, for the past 24h I had zero problems.
I know that maybe this is a not so common situation (using US phone outside with an international sim card), but if you are like me, then this steps will turn your phone back to normal.
I hope that you will find this info helpful!