I am not aware of any PTZ that can output LOG files outside of the new UHD Panasonic. IMHO, you'd be better off by starting with the same cams using the same white and black balances and then using the proc amps to paint as needed. For a livestream, the standard (non LUT) workflow is easier and cleaner than adding a LUT. Not to mention easier on the CPU. I guess if you're going for a super specialized look then a LUT could be useful, but I've never seen (or been asked for) that sort of thing in a livestream
I have found a solution.
Now we feed OBS with Mix1 and use the lut function.
Not happy that i have to use third party tools, but its working
For incoming calls i use V-MIx call for now. Maybe something like this works in a tricaster in the future