A very long time? Gosh there are still LCD's from the early 90's that still work as long as you take care of them. And not too sure if there is a definite way to test their life span :/
I have a first generation 19" Acer monitor that still works perfectly...it's pre wide screen but has no dead pixels and makes a great second monitor...I'm guessing but I think it's around 14 years old
The backlights are rated to last at least 30,000 hours (about 3.5 years of continuous use), in my experience they last much longer unless they are damaged. Eventually some pixels may die but they are surprisingly resilient.