One small point before touching the question in the title, that is the title of the movie. For those who didn't put too much effort into their Greek mythology studies. Styx is the name of the river leading from the land of the living into the land of the dead in the Greek mythology. Even more important is the fact that passangers on that river must have money with them or they won't be allowed into the land of the dead and will remain on the river for a century, in a greek version of Limbo.
Now that the movie's title makes sense, I'll discuss my own title. When a director chooses a lean approach to movie making, it means not using camera tricks not using any CGI, but rather making his own presence and the cinematographer's almost unnoticeable. And that's exactly what Wolfgang Fischer does, that is apart from two early scenes in the movie involving monkies. And in my humble opinion the movie would've been better without these scenes.
One last point: when one chooses a lean approach to directing it usually calls for a lot more from the actors. We get only two in this film, and the two of them are superb. Susanne Wolff and Gedion Odour Weseka, don't act their roles, they are the characters they portrey.