Have you tried unplugging the HDMI cable from both the LG G3 and the TV and then plug everything back to allow the devices to renegotiate the signal?
You may be using an uncertified adapter. You will have better luck with the certified SlimPort HDMI SP1004 available on Amazon, search for SlimPort SP1004
There is also a new product called the SlimPort NANO.CONSOLE that just launched on Indiegogo – it lets you connect your LG G3 to the big screen, simultaneously charge your LG G3, and remotely control your LG G3 with the included Bluetooth Smart touchpad remote. It’s really useful and plug-and-play easy to set up and use. Please check it out on Indiegogo by searching on "NANO.CONSOLE".: