They are just encodings defined by a curve and a matrix, freely available in white papers from most manufacturers (except shitty ones).
Some examples:
https://dl.fujifilm-x.com/support/lut/F-Log_DataSheet_E_Ver.1.0.pdf
https://pro.sony/s3/cms-static-content/uploadfile/06/1237494271406.pdf
https://www.arri.com/resource/blob/31918/66f56e6abb6e5b6553929edf9aa7483e/2017-03-alexa-logc-curve-in-vfx-data.pdf
How MLV App implements them:
https://github.com/ilia3101/MLV-App/blob/master/src/processing/image_profiles.c
There's nothing illegal about encoding your footage to interoperate with a LUT or a grading tool ;)
QuoteAre they really from Sony/Arri or are they just very similar?
You'll never get the same output from these cameras as you will from a Sony or an Arri, the sensors are different, and processed differently before it even gets to the log. But it's probably close enough.