Mustafa, I haven't looked around Open Source Software lately (GIMP is Open Source and Free), but I'll bet if you dig around in Sourceforge (
https://sourceforge.net/) for a while, you could probably find a way to use these resources independent of Photoshop.
Here is a discussion of attempting to use a 3D LUT in GIMP...
http://discuss.pixls.us/t/gimp-how-to-apply-3d-lut/1567
Here is a very powerful open source imaging toolkit:
www.imagemagick.org
There are a TON of videos on Youtube dealing with converting LUTs between various formats AND covering many open source LUT creators and converters. Start here:
It's not going to be easy, but it should be possible to use LUTs in GIMP if you find the right way to convert them to a format GIMP can understand.
The webpage you referenced is written in Java.
I wish I had the time right now to explore this subject in depth, but I don't; Sorry! I'll attempt to do some research when I get the time, but between work and a crazy personal life, it's problematic!
Cheers.