I am editing a short film . I shot the film with alexa logc proress 444.
The project is for film theaters and my question is shall a grade the log c without an lut or to apply an lut and then grade it?
In case that the answer is without lut shall I make a different grade with lut for the dvd version?
Complicated question. In a nutshell, you MUST use a LUT.
But which? And where?
Case 1: no LUT.
Open the file, view on your display. You'll see a washed out LOG image. If you grade from here and get it to look good on your display, you've created your own LUT. And you're no longer working in log, but in your display color space, probably rec709. To out put to film, you or your lab will need to apply a LUT to covert back to log space for filmout.
Apply a LUT in your grade to de-log the image, then grade normally. Arri has a site where you can create these luts. This approach has the advantage that the correct matrix transform is applied to your arriogc original file. You will then be grading in your display color space and you will also need to convert again to log space to output your negative as above.
Apply a display calibration LUT to alter your monitor view to emulate the film print. This LUT does not change your file, so it is the only way to grade in log space as Gary recommended. When you render out this version it will already be in log space and adjusted for filmout. But now, you will need to create a new grade to work for electronic displays. This will require another grading pass like #2 above.