It's just not possible.
Setting your smartphone aside for a moment, even assuming you have an extraordinarily stable WiFi signal, transmitting audio over WiFi would introduce enough latency to ruin your day.
In some cases, the transmitter side could introduce a delay on the video stream to compensate for the audio delay (forget about gaming or anything like that in this case). Your LG TV might have a "AV Sync Adjustment" option, but even then, this might not be enough.
In any case, your TV will not cast audio by itself and here we come to your "second phone" as transmitter. The phone is unlikely to have a line-level audio input, and even if you still have a phone with a 3.5mm audio jack, that is a microphone input. To make things worse, this input is MONO.
I don't want to buy more devices
rules out any other type of audio input adapter for your transmitter phone. I'd say this is a dead end.