Please be aware that most of the users that are experiencing this issue with "lock lag" or "wake lag" have an SD card installed. I had a PNY 16GB Class 10.
I noticed that I too have been having an issue lately, as my Note 3 decided to stop recognizing my SD card. However, I did not remove the card and tried to recover it through the phone itself. When that didn't work I figured what would be the harm of leaving it in the phone even though it wasn't being seen by the device itself.
That posed to be the biggest problem, as the phone and the SD card were interfering with one another, and caused the screen to take up to 4 seconds before it came back on upon wake.
Nothing seemed to alleviate the problem if I had widgets or a password or messages or shortcuts turned on or off... it didn't matter until I REMOVED THE SD CARD COMPLETELY!
Although you should still follow the other steps to improve device speed, ensuring that your SD card, whether it works or not, is removed to exclude this is as the overall problem, as I myself have experienced it firsthand.