James Miller ran a test in which he recorded externally from GH5 with Vlog and he either applied the LUT in post or baked it in.
Even with an external recorder that offers high bitrates and very good codecs, the difference is quite big. See the color smearing ('YUV chroma smearing' ?) in many places and the color shifts in the shadows. I believe using baked in LUTs with external recorders should give better results with any camera with an HDMI log output.
I hope Panasonic implements