Can't give you an exact answer without model numbers.
1. If the TV has optical audio out and the LG has optical input you just need a Toslink cable. On many TVs you may have to turn the optical output on, the TV speakers off, and change the audio output type in the TV menu.
2. HDMI ARC allows you to connect the soundbar to the HDMI-ARC input on the TV. You need ARC in both the TV and soundbar and it has to be turned on in the TV menu.
3. Headphone output to aux input on the soundbar.
4. You may need a converter like one of these http/www.parts-express.com/parts-express-dac-digital-to-analog-converter-(51-compatible)--180-999