Starting an app when the screen is locked?
There might be multiple solutions to this. One I can think of involves the use of Tasker, the most flexible automation tool for Android. You could create a profile that triggers on "Screen Unlock", and have it start an app.

However: though there's a free 7 day trial available on the projects homepage, after that the app costs about 5 Euro. There are many other automation apps available on the playstore which might be able to achieve the same. As a long-time Tasker user I no longer try the others, so I cannot tell for sure.

Condition: Event &rarr; Display &rarr; Display Unlocked
Task: App &rarr; Load App &rarr; (select your app here)