I believe the GH5 has the ability to send the LUT applied footage out through hdmi so should be able to record baked in with an external recorder, not sure why you would? except James Miller @vimeo has had some interesting results with baked in (better looking) than post applied LUTs.
I know Monet, this is not Monet. And I have lived in Berlin, and it's an okay city but you don't become an artist because you move there. It's full of angry poor young people complaining about newcomers stealing their jobs. It's confusing me when you're putting pretentious prose and soft generic music in a test video for a lens and calling it filmmaking. There's no balls here, just filming people without them knowing usually from a distance. (Insert ironic smiley here to deflate any hurt feelings)