I too am experiencing issues with my LG G3 post-lollipop update. Issues so far: battery draining at a higher rate (35% in 6 hours overnight with phone 'asleep'), notifications not working on Wifi, Facebook not working at all on wifi, general browsing slower on Wifi.
I did some digging and it appears to be an issue with IPV6 and how it is implemented in android 5.0. This apparently affects a lot of other phones, and is not just a LG / VZ problem. IPV6 cannot be disabled unless you root. You may be able to fix IPV6 on your wifi network, so that's a point of focus. My work wifi is also problematic, so I don't think I have a lot of recourse other than to call Vz for a new phone still running 4.x
Here are some interesting links
Wifi slow on lollipop - google dev states it will be fixed (comment made 3/2)
Issue 79576 - android - Wifi slow if IPv6 enabled - Android Open Source Project - Issue Tracker - Google Project Host…
Summation and testing showing IPV6 is the issue - includes fix if you are rooted (mine is a work phone, so I can't)
Fix Lollipop wifi issues (and coincidentally the Facebook app) by disabling ipv6 : Android
General article about issues across carriers
LG G3 Android 5.0 Lollipop Problems Reported By Users: Battery Drain, Slow Charging, Wi-Fi Issues And More : PERSONAL TE…
Disheartening with so much info available the first level support team has not been given the directive to acknowledge the problem and provide info that a fix is inbound (or not).