With the built-in tools, no. There are third party plug-ins for LUTs that might include additional functionality. Otherwise, you'd need to get the entire effect into one instance of Lumetri.
yes, any program that can export out trillions of colors in PNG format for a HALD image can create a 64 cube lut with with this free lut creator
IWLTBAP LUT Generator
some things you can't burn in correctly are sharpen, secondary color correction and keying. but you can bring in clarity.
Red Giant's old free tool LUT Buddy can do this. Takes two instances of it, on on an adjustment layer above everything set to writ pattern, one on the bottom track clip in the ECP below all other color correction set to read.
Then go into the LUT Buddy control settings in the ECP for that bottom one, tell it to export LUT.
I don't have the link on my phone but I still think search of the Red Giant website can turn this up.