Can I change the window lock screen “reset password” application?

If you use Forefront Identity Manager (FIM) Self Service Password Reset, there is a reset password link on your windows 7 lock screen that opens the FIM password reset application:

Is it possible to edit this link, so that it opens a self developed application?

Yes, it is possible.

It is also not incredibly easy to get to work reliably. This is partially by design, because by altering the Windows Logon process you could also lower or bypass security.

In short:

Windows 2000/ NT/ XP
Replace MSGINA.DLL in the registry with a custom DLL and update the registry.

Windows NT 6.0+ (Vista+)
You need to create a custom Credential Provider.

If you research this further you will see there are many examples and tutorials. Neither route is exceptionally easy.