They can last from 1 year and up to 10 years and beyond. I've had some cheaper monitors fail me within 2 years and then I have a dell lcd computer monitor that I bought in 2006 new that is still working fine today.
Although that's not an led monitor. I expect the led monitors should last longer than the lcd monitor I have.
If you use your monitor more and subject it to bad conditions such as too much heat,smoke etc then it's lifespan could be shortened.
Take care of the monitor and you should get at least a decade out of your led monitor.