I have a 99 cl 3.0 and I recently had to replace the passenger side window regulator (the motor was shot). I replaced it with a Dorman. When I took the door panel off I found a plastic cover on the door. Obviously this did not come off well. I still have it and repaired it with tape but I did not put it back after replacing the window regulator. Is this cover necessary? Does anyone know what its purpose is?

Also, the passenger side window squeaks sometimes when being lowered. Is there a way to stop this?

 

I think the plastic serves as a moisture barrier.
To help with squeaking, get some silicone lubricant and spray it along the window tracks. Some other kind of grease may be better, I don't know. It seems like something thicker would do a better job, but all I have is silicone.
I found out the last time I replaced the motor/regulator that you can get great access to the whole window track when you have the door opened up like you did. You don't have the plastic on now, so if you remove the interior skin, you should have this good access still. With the window up, you can peek/reach inside and pry the track open a little and spray it down good.
To do the top of the track, you don't need the door apart. Just put the window down and spray the tracks good.
It may squeak a little more the next few up and downs, but once it gets spread around good it should go away.
It's probably good to attend to the squeak quickly when it shows up again, because more friction means more work for that window motor.