If your phone was working fine with 4.4.4 then it sounds like Lollipop screwed up when updating.
Best bet is to download the factory image from google, and flash it yourself using something like wugfresh nexus root toolkit which is probably the easiest way to flash your nexus and see if the problem cleared.
Sadly, my phone is still freezing and rebooting after a factory reset. I'm going to try to install kit kat on it later today. Actually, I'm going to contact google support first and only try going back to kit kat if they deny my rma, since I shouldn't have to revert.
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