Long-press on an icon and slide it up to Remove. It will then be returned to the app drawer. Or slide it to the edge of the screen to move it to another screen.
You can reposition apps according to your preferences, by long-pressing, sliding them to where you want them, then letting go.
Unfortunately, this advice only works on the home screen, not the lock screen.
Screen Lock (accessed from Settings/ Security/Screen Lock) only gives the options of:
None
Long Press
Pattern
PIN
Password
If "None" is chosen, there is of course no lock screen at all. If any others are chosen, the only actions allowed are the unlock itself - which leads to the that screen disappearing altogether, or the opening of one of the apparently fixed icons.
The manual does not address this at all.
I see only two things that can be done with the screen lock, and only two ways to access it:
1) You can set the WALLPAPER for the lock screen by long pressing a blank spot on the home screen. That pulls up options for Widget, Apps, Wallpaper, and Effects. Select the Wallpaper tab, and there are home screen and lock screen options.
2) You can set if you WANT a lock screen, (and HOW to open it if you do), through Settings/Security/Screen Lock.
I have been completely unsuccessful in finding a way to edit/change the useless (to me) icons of camera, email, and contacts, to more useful ones such as messaging, voicemail, and the calculator.
I'd honestly rather have no icons on the lock screen than useless ones, so I will probably just disable it.