Android
Set a Different Wallpaper for the Lock Screen auf Android
Android treats the home screen and lock screen as two separate wallpaper slots. Tapping and holding the home screen to change the background usually only updates that one screen, which is why the lock screen keeps its old photo.
To set a dedicated lock screen wallpaper, go through the wallpaper picker instead of the quick shortcut: Tap on Settings ➔ Tap on Wallpaper & style ➔ Tap on More wallpapers ➔ Choose a Category or tap on My photos ➔ Select a Photo ➔ Adjust the Photo and tap on Set Wallpaper ➔ Tap on Lock screen.
This flow lets you crop the photo separately for the lock screen preview, which has a different aspect ratio than the home screen once widgets and the clock are placed. If you want the same image on both screens, choose the option that applies it everywhere instead of picking Lock screen only.
On devices with an always-on display, a busy photo can make the clock and notifications harder to read. In that case, a simpler image or one of the built-in categories usually works better than a personal photo with a lot of detail.