Export from LUTly, install, apply. Three steps and one setting that matters.
Export your .cube files from LUTly.
In Lumetri Color: Basic Correction > Input LUT > Browse. Pick your .cube.
For many clips, put the LUT on an adjustment layer above them.
Do not stack the LUTly LUT on top of a separate log interpretation or a second input LUT. One conversion, done once.
Input LUT. The LUTly file contains the log conversion, which is Input LUT's job. Creative Looks sit on top of already-corrected footage.
Log footage is flat by design. The LUT contains the conversion that restores contrast and colour.
Use an adjustment layer above the clips.