I rarely advocate for someone to lose their job unless it's a case of extreme incompetency to the detriment of others or a case of extreme ego taking over the functioning of a persons ability to do their job. In either case or any other scenario, if the person is not capable of doing their job and it's hurting others, then outside of retraining and trying to get them back in line, you have to let them go. Keeping only diminishes the credibility of the organization who employs them and takes away from the other employees who are good at their job and puts them in the same basket which causes even more discord within.
By whatever metric you use, Chriss Lee should not be an NHL referee as he's shown he's wholly incompetent for several years and in several different scenarios. He's got to go of the NHL hopes to maintain any semblance of integrity which has already been called into question multiple times and now has a reputation for being a bush league with the worst officiating of any other major sport.