The GPS issue is actually a hardware issue. There is a springy connector on the phone that tries to keep a steady connection to the anttenae strip on the battery cover. It is on the side opposite of the SIM card.
Here is a picture from another XDA thread by JTNiggle that shows the insides of the VZW LG G2.
First picture shows the battery cover and you can see the small square copper connector for the GPS antennae on the right hand side. Second picture shows on the right side of the phone above the battery the little springy copper connector for the GPS sensor on the phone. These are the two areas I used very tiny pieces of electrical tape on to make a solid connection. This has 100% resolved my issue with GPS signals and I have been sporting this change for over a week now. I get a signal lock between 3-7 seconds depending on where I am at (inside or outside) and the days weather. I have done this on a total of 4 phones now and all four phones no longer have GPS signal lock issue. Just make sure you use a non metal tool to pop the battery cover off so it doesn't scratch up the shiny silver bezel strip.
---------- Post added at 09:52 AM ---------- Previous post was at 09:50 AM ----------
Originally Posted by cckeeler
I have been going back and forth with Verizon and the GPS on my G2. I actually have my third replacement phone waiting for me when I get home. The last rep I spoke with said that it is a known issue that is to be fixed with an upcoming update. I would assume that update to be 4.4.2 but I haven't heard whether or not the GPS is any better in the leaked OTA. He did tell me that they have received the update from LG but it was currently being tested.
I honestly don't think all the software updates in the world would fix this problem. It is a physical hardware issue that is causing the problem.