Same. My Verizon LG G2 was a fast, smooth phone to use. I rarely had to reboot it, the battery would last on average of 2 days between charges, and was an all around great phone. Then I got the Lollipop upgrade. Since that dreadful day, my phone battery started dying in less than 12 hours, my phone would be hot, the location services stopped working properly, texts would take up to 5 minutes to send, it was horrible. I was ready to smash it with a hammer!
The only way I found to get around the problem was to disable my Wi-Fi connection. When I was away from work or home, it would constantly search for a Wi-Fi signal, causing the phone to heat up uncomfortably, and to drain the battery super fast. Now I only enable my Wi-Fi if I am at work or home, and only if I'm going to use it for something that will take a lot of data, such as application updates.
I close all apps when I'm done using them. I also reboot my phone every couple of days to completely clear out anything that might be running in the background, even with all my apps closed. To this day, every time I reboot my phone, it tells me that it is optimizing apps for Android. Now, at least, I can get about 24 hours of battery life out of my once great phone. Counting the days until I can upgrade to a Note 5!
I had the same problem. I had loaded task killer and battery protectors and learned that the Android system keeps these apps open in the background. I uninstalled the task killer and battery apps and the phone now stays charged for 24 hours if no exceptional use. I recommend uninstalling any apps that kill apps or claim to improve battery usage. Also my phone no longer gets hot as I think these apps were constantly putting demand on the processor.