Is there any way to update a rooted Samsung Galaxy S4? Currently I have Lollipop 5.0.1. I have tried Samsung Kies, but it shows a message that the device is not compatible.
This doesn't resolve your "device is not compatible" issue, but your Galaxy S4 is already running the highest version (5.0.1) of Android available for it. This appears to be true regardless of what model you have1. The last updates for the various models/regions were rolled out in early- to mid-2015, and there likely won't be any further "official" updates.