OS X 10.11.3 Update, keyboard lagging
I would try to disable some keyboard-related applications, if you have any. Such as:


Karabiner
Text Expander (I had one as extension for Google Chrome =)
Punto Swither
etc.


I have just got rid of the keyboard lags on my system by uninstalling all of these (it could be only one of them that caused the issue, but I've shot all three).