Share your experience!
That's an odd behavior, do you have any taskillers? third party home launchers or lock screens? antivirus?
Try turning your device on in safe mode, and then check
This is how to boot on safe mode (lollipop)
http://talk.sonymobile.com/t5/Software-Updates/Lollipop-New-Features/m-p/955490#U955490
Maybe you should just bite the bullet and perform a factory reset or a repair install via PCC, I had to perform the repair install myself for other problems and now my phone seems to be working great 😉