No...
DVI does not carry audio.
You will need to connect separate audio cables - assuming it has speakers.
That monitor does not have a video port that carries audio via the same cable.
Based on the info you provided above, the monitor has no audio input.
Alternative option: buy an Apple TV. You can mirror your screen on the LCD monitor through the Apple TV (video and sound) using AirPlay (so fully wirelessly) plus you get all the other benefits of an Apple TV!