"Lag" is very subjective and really depends on what you expect to happen as a result of a particular function event.
There is a very noticeable delay when powering the phone up, I might call that Lag, but the O.S. is not fully loaded so that is unfair.
Some apps do not need any outside information and will just pop open immediately ready to go to work. The calculator is one example of this. "The Weather Channel" is an example of an app that needs a LOT of outside information before it can be fully functionable, so you might say that The Wx Ch exhibits a lot of lag.
The way the screens function really effects overall response. For me, I turned off anything and everything that is not needed.
Animations:OFF
Motion detection:OFF
Background apps (S Health) turned OFF (these run all the time and take up CPU time)
Screen backgrounds that are frilly and have motion in them, OFF:
I use a solid Black Background because it is easier on the eyes, and has the least amount of CPU time needed.
I use Nova Prime as my launcher because (to me) it seems more responsive than the native TouchWiz launcher, and it damn sure has a hell of a lot more features available to you. ie, it will continuously scroll around and around, unlike TW which stops and forces you to backup.