Yes, one option is to get a Cine-D to Rec. 709 LUT, possibly from Panasonic but there might be third party ones that some prefer. Also, since the advantage of log is greater flexibility of color grading you also want to use the Color Grading or Levels video filters. However, since Shotcut’s CPU effects engine is 8-bit integer I think you should place the LUT filter after these filters. Otherwise, the LUT might cause clipping that you were trying to avoid by using log.
The GPU Effects mode uses 16-bit floating point but it currently lacks a LUT filter. So, attempting to use that combination can result in some clipping or quantization loss (information slightly inaccurate due to the low precision of 8-bit numbers).
Another option is to shoot some same things in both Rec. 709 and log, and then use Color Grading filter without a LUT to develop your own base preset. The goal is to have a preset that you apply to your log footage to bring it very close to Rec. 709. Then, for each shot you apply the preset and fine tune it for that exposure. That way you avoid 8-bit integer degradation between successive filters. This works both with and without GPU Effects, but with GPU Effects and only using GPU filters you can read and export 10-bit without any degradation.