If you don't use S voice open it up and go to its settings and disable the home button checkbox. This will pretty much get rid of the home lag when pressing the home button. Also disable the animations as shown in the video and this will essentially fix the launcher lag. On mine I was getting a lot of hiccups from the wimamp 4x1 widget and removing that made my phone smooth in combination with these other things.
It should be said that my phone lagged significantly all over the place as it came from the box. The video up above shows a good representation of that and I saw it on both S4s I saw in the store and you can see it in many of the video reviews even when the phone is on final firmware. If you buy this phone you should expect some lag in the launcher and with opening and closing apps until you make some changes. This is not a case of something being overblown on forums, its real and you will have it unless you buy at a later point where a firmware update has fixed it.