You cannot make the lock screen or the home screen that clean. The lock screen displays the time and other things. The home screen has a dock. That person is displaying a photo.
Open the Photo app, select a picture, zoom it at fullscreen and leave it open.
But joking aside, why would you want a homescreen with absolutely no icons?
For example, my homescreen does not have "Slide to Unlock" on it (I'm on iOS 9) because I do not care for the look of that. However, the action of that mechanism is still present.
I get a cleaner lockscreen but still have the stock functionality.