If your TV supports screen mirroring, that's the way to go. The downside is you'll be draining your phone's power because the screen stays on the entire time.
The most efficient way is to get an HDMI cable and hook that up to your TV or an AUX cable that hooks up to your Home Theater system separately.
But I was under the impression that there WAS a Spotify app for LG TVs. Of course, for this you'd need a Premium account and it loses a few features (radio).
And last, but not least, Chromecast. However, the Spotify app doesn't natively support Chromecast. You'd have to either download an app I believe exists, or you'd have to go to Spotify's web player on your phone using the Chrome browser and THEN send the audio to Chromecast. In reality the connection is handled by the Chromecast dongle, so you can really free up your phone to use on whatever else you need.