Sound from an Apple TV plugged in an LG monitor
The answer is both Yes and No depending on the model. Let me explain.

The model you have linked to at http://www.lg.com/hk_en/monitor/lg-IPS277L is the Hong Kong model and this has a headphone socket. However, if you were buying the model from another country (let's use Australia as an example) it may not have the headphone socket: http://www.lg.com/au/it-monitors/lg-IPS277L-ips-monitor

The model you have linked to is now discontinued, but you can still access the manual downloads etc from: http://www.lg.com/hk_en/support/support-product/lg-IPS277L

If you download the manual it seems to confirm the headphone socket exists, but does not make any real mention of this anywhere. However, the same manual is used for both the LG IPS277L and the LG IPS237L (they are identical, one is basically the 24" model, the other the 27" model).

Now, if you happen to read the review on this page about the LG IPS237L, it is clear that for this particular model you can do exactly what you want to do. 

I suspect that as long as you have a Headphone port you will be right.