Not all Galaxy S4 devices are affected by this issue, when you use the stock Lock Screen (Samsung ripples) or TouchWiz you might see lags due to Zooper Widget. This is a Samsung Bug as other Samsung phones (es the S3) with the same launcher or lockscreen are not affected at all, someone reported that even Advanced Clock Widget has this problem (which is completely different).
Thanks to debug logs received by users i also can confirm that lag is present when unlocking even if the widget is not updated at all (so if it is just on screen). The issue has been slightly mitigated on latest builds by forcing software rendering on S4 terminals, this is however not a complete fix, as of today the only workaround (and a speed up in general) is described in video below (thanks MADDtec), i also hope Samsung will release a better firmware soon, finally if someone able to use ADB wants to help me please please please send an email to firstname.lastname@example.org!!!
If you do not want to check the video here is what it does:
- Settings -> More -> About -> long press "Build Number" 3 times (dev mode goes on)
- Back -> Developer Options
- Set Windows Animation Scale to Off
- Set Transition Animation Scale to Off
- Set Animator Duration Scale to Off