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I think this problem may be specific to Android 5.0.2. because the instructions in the user manual no longer work.
I installed Extended Controls (great app/widget) and it seems to add it's widget to the lock screen (I have the widget on my Home screen but I added that myself). Anyway for some reason I ended up with two identical widgets on my lock screen and they take quite a bit of space. So I decided to remove one of them. I followed the instructions in the manual but found them impossible. I press and hold the widget but can't move it on it's own. It is very difficult to move at all and when it does everything else moves with it. Plus the upward swipe needed to get to the rubbish bin (which never appears anyway) unlocks the phone so I end up on my Home screen and the widget on the lock screen has not been removed.
How can I remove widgets from the lock screen?
If you are using Sony's lock screen you can't, you can only change the lock screen watch, or you can download a third party lock screen app.
QUOTE from the user manual
To add a widget to the lock screen
1 From your Home screen, tap , then find and tap Settings > Security
2 Mark the Allow widgets on lock screen checkbox.
3 To lock the screen, press the power key.
4 To activate the screen, briefly press the power key.
5 Swipe inwards from the upper part of the screen until appears, then tap it.
6 If required, enter your PIN code, pattern or password to unlock the screen.
7 Find and tap the widget that you want to add.
8 Follow the on-screen instructions, if necessary, to finish adding the widget.
The items that appear when you tap are available by default and cannot be modified.
To remove a widget from the lock screen
1 To activate the screen, briefly press the power key .
2 Touch and hold the widget that you want to remove, then drag it to .
The camera icon at the bottom of the screen is there by default and cannot be removed.
This clearly says you can. As I said, it doesn't work. Why not? There's no Allow widgets.on lock screen either. Why not?
Because you are on lollipop not on kitkat. Google has changed this, you can't have widgets on the lockscreen any longer unless you use a third party lock screen app.
You can google it and find articles such as this