The American Idol runner-up features in a sci-fi-influenced clip, where he finds himself in a futuristic medical facility where everybody completes the same dull tasks.
Lambert eventually manages to lead a revolt inside the facility and escape the complex, leading a dance routine at the close of the video.
'Never Close Our Eyes' is the second track to be lifted from the singer's upcoming album Trespassing.
Trespassing is the follow-up to Lambert's 2009 debut For Your Entertainment, to be released in the UK on July 2.
The album secured Lambert his first Billboard number one LP last week with sales of 77,000.
He will perform a set of London Hammersmith Apollo shows with rock legends Queen on July 11, 12 and 14.
Watch Adam Lambert answering Digital Spy readers' questions below: