I've had the same problems - getting a black screen and only seeing notifications and the 3 buttons, and not being able to get out of that mode unless rebooting. Then just opening an app and pressing something like Home got me there again.
It started a few days after installing Lollipop on my rooted Nexus 5, which I did about 2 weeks ago using Nexus Root Toolkit to flash back the stock recovery, I had TWRP, and then installing the OTA the normal way. This way I got to keep all apps+data.
When it happened the first time I tried rebooting but same thing happened over and over for hours. First after about 3 hours it stopped and everything worked fine, very strange indeed. Then it took about 2 days and started happening again.
I got tired of it and thought it had something to do with me not factory resetting the device (wiping cache+user data) after installing Lollipop so I did that. After only a day I started getting the same issue again. I tried wiping the cache directly, same problem. I could only do a few actions (eg. opening drawer and uninstalling an app) before getting a black screen. I started searching and found this thread and realized it might be some app causing it. Since several people blamed Tasked I uninstalled that and rebooted, didn't help. It could still be Tasker for some people I think depending on what rules you have set up. The next suspicious app I had was No Lock Screen, com.futonredemption.nokeyguard, (I'm not allowed to link) which I uninstalled. After that I haven't gotten the black screen again, tried rebooting also and nothing yet. Since it disappeared right after uninstalling I assume that app was the culprit.
To verify I reinstalled it and gonna see if the problem comes back. I'll let you know!
I recommend people having this issue and having apps that do stuff related to the lock screen do uninstall them one by one and see if it helps.
If you find one like I (hopefully) did, list it here and we can together understand this problem and hopefully make app developers or Google change how things work so this can't happen.
Cheers