Check if you lg tv support any of technologies like dlna, mirror technology or airplay. If yes hook you tv to wifi router and your phone to wifi router and then you can wireless stream from your mobile to your lg tv.
DLNA n mirror technology are supported by android smart phones an airplay by apple products.
You can also check your lg tv have WiDi - Wifi Direct, you can also connect wireless this way.
if you tv is not smart one and don't support all above technologies then buy an usb or hdmi android dongle which support all the above technologies and you are ready to go.