No, it isn't. Hero Dog: The Journey Home is a work of imagination. The story was crafted to evoke emotions and tell an engaging narrative that isn't tied to real-life happenings.
Not likely. Usually, movies labeled as such are not strictly based on true events. 'No Escape' might incorporate some common themes or scenarios but is likely not a direct retelling of a real story.
To know if 'The Lie' is based on a true story from Wikipedia, you'll need to do a search on the platform. I don't have that info off the top of my head.