Can we launch applications from the lock screen itself?
I am using a Nokia Lumia 520 with Windows Phone 8.1.10.
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In addition to launching apps from notifications in the Action Centre, as mentioned in RIPS10's answer, you can also launch a camera app of your choice by holding down the camera button. I don't know if any third-party apps support this, but theoretically it might be possible to have an app that registers as a camera app but actually can be configured to launch another app. Not sure if anyone has looked into doing this yet.
However, both of these solutions actually rely on some other feature that's available independent of the lock screen. It's not possible to make the lock screen itself interactive and launch apps.