Current when I choose a photo to be set as wallpaper, my lock screen's background is automatically changed to be this new one.
I want the lockscreen to keep its old background, how can I do that?
I'm using Google Samsung Galaxy Nexus.
You can't do that. But what you can do is download a third party locker such as GoLocker: https://play.google.com/store/apps/details?id=com.jiubang.goscreenlock&referrer=utm_source%3Dgoogle%26utm_medium%3Dorganic%26utm_term%3Dgo+locker
This is what you need to do, supposing you're on a stock ROM:
If you have a custom ROM, you should check the forums of that ROM to see if its supports this.
Although I am on another device with another android version (HTC Desire HD / ROM: JellyTime R9 (Android 4.2.2)) I think the problem may be the same.
In gallery I can only set the images as background. But I can set a different lock screen background image in system settings. I think this options depending on used Launcher/Lockscreen and are also valid in stock roms. I am using NovaLauncher and I can only set a different lockscreen image that way as far as I know.
Sorry for being that fuzzy.. What I really wanted to say:
In Android 4.2.2 (can't confirm atm that it also works on 4.1 due to lack of working emulator) - depending on launcher/locker - just do this setting under the proper category in system settings ..