The culprit that delays the action of home button in Galaxy S4 is its built-in voice assistant app S Voice. In GS4, double taping the home key will launch S Voice. That means, every time you tap the Home button, your GS4 is waiting for the next tap to see if it needs to launch S Voice. If you aren’t a frequent user of S Voice you can fix the delay of Home button action by disabling “Open Via Home Key” option from S Voice settings menu.
How to Fix Galaxy S4 Home Button Lag
Open up the S Voice app, tap Menu button (usually on the left of Home button), and tap “Settings”. Then uncheck the option “Open Via the Home Key”. That’s it.
Note: To launch S Voice, either you can straight to the app, use it as a widget on home screen.