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.