Well, I don't have any Sony cameras so can't help you out there. The lut is designed for ML Cinelog footage. However, if you'd like to use it with your Sony I would suggest first making a lut to match SLog2 to Cinelog in terms of tonality and colour. Then apply the Ektar lut. I did this with my XC10 and now I can match that easily to my 5D3.
Here's how I did it:
1. Load up a white image on your monitor
2. Colour balance each camera against the white image and slightly defocus
3. Find the point at which each camera clips highlights 100%
4. Take a series of videos, lowering by 1/3 stop each time until you get down to 12 stops (36 videos)
5. Denoise and blur each clip
6. Separate them out into individual squares, arranged horizontally. Now you have a map of the tonality of each
7. Use curves to match one to the other (split-screen one on top of the other and match the curve on the waveform)
That's the first step. Once tonality is matched, it's time to match the colours. See my post above on how to do that. All of this takes time, of course, but it's a great skill to develop as you will be able to match cameras fairly closely. Here's how my Ektar luts look on the XC10:
When I shoot it side by side with my 5D I can slap a lut on the XC10 and it matches pretty closely. Looks like you got a close match from your screengrab - maybe you can use that correction in future?