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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.:cool:
But joking aside, why would you want a homescreen with absolutely no icons?
 
But joking aside, why would you want a homescreen with absolutely no icons?
Minimalism.

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.
 
Um, pretty sure that’s a photo being shown not the lock screen.
 
iOS allows you to leave the first page blank of icons... but you cannot remove the dock shading, even if it is empty of app icons and folders.

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