To lid or not to lid? I'm currently making a plain chicken broth with the carcasses. It's currently at a low simmer and will be for the next few hours.

If I place a lid on the pot, will it affect the clarity of the broth somehow? I have in the back of my mind that placing a lid can make it cloudy for some reason, but I'm not sure if my mind is making up things or if this is a cooking myth or if it is actually the case somehow. 

Leaning towards either cooking myth or my brain making things up again.
What makes it cloudy is a vigorous boil. You want to have a gentle simmer. If you put a lid, it can certainly make it boil (the temperature will be higher, as it has less heat exchange), so it's not a myth. 

You are the one who knows what temperature your pot reaches after hours with and without lid. If your temperature is so high that a lid will cause it to boil, leave without the lead. If the temperature is so low that without a lid, it might get too cold to simmer and head towards the danger zone, use the lid. Only your experience with the exact same setting on the exact same stove, the pot you are using and the amount of liquid in it can help you predict how hot it will be. 

If you are there to watch the pot and adjust it now and then, then just adjust as needed.