Of the issues mentioned, I'm only experiencing the heat... it's not something I had with my old Note 2, but this phone is a gazillion times faster, the screen is far brighter, and the screen has a far higher resolution. So my feeling is that the heat is the price you pay for all that power. However, if it was metal casing, the heat would probably dissipate faster. (Here's a recent AC article doing a heat comparison between modern flagships:
A look at the One M9, S6 edge, LG G4, and Droid Turbo through the Flir One | Android Central ).
I'm not getting any lag, but I understand (from reading nearly every G4 forum post) that lag may be due to carrier software issues.
For battery, I'm very happy with it. I can get 24 to 30 hours of standby time (if I do a clear-all frequently), and I usually get around 3.5 hours of SOT. For both battery and heat issues, I highly recommend doing a "clear-all" to calm the phone down.
As a means of moving in the right direction, if you choose to stay with the G4, please read through the Common Issues and Solutions sticky (
http://forums.androidcentral.com/lg-...solutions.html ) where there are both Lag and Heating thread links. I suspect, however, that you've already done that.
EDIT: One more thing to try, re: keyboard lag... do you have a bunch of screenshots in the clip tray? If so, try deleting them from the clip tray and see if that helps.