Definitely not. 'Secret Society' is a work of fiction. It doesn't draw from any true stories or actual occurrences. The plot and characters are all fabricated for entertainment purposes.
Yes, it is often the case that such a title implies it's based on a true story. However, without more specific information about this 'Secret Society of Lies', it's hard to say for sure. There are many works that claim to be based on true events but may have elements of fictionalization added for dramatic effect.
The movie 'Society of the Snow' is not a true story. It's a work of imagination and creativity. The scenarios and characters were developed for entertainment purposes and not drawn from real-life happenings.