All the patches have standardized Lab values, which you can translate to any color space you want, or Lightroom % if you like. Just google it. Then you can use the patches as reference in processing.
I use a colorchecker chart to set the tone curve this way, for art reproduction. I stopped bothering with any profiling software long ago, I was never able to improve on the Adobe Standard profiles in any way, for any of the cameras I've tried.
D Fosse I know you have considerable experience with art reproduction, but you've given the OP only a thumbnail sketch of what's required. I agree Adobe Standard is pretty darn good, but how did you go about correcting the camera profile (or image) to match the patch standardized Lab values. My first thought is to use the Adobe DNG Profile Editor with the CCPP calibration image and manually correct the Tone Curve and each of the color patches to match the standardized value. Then save as a new custom camera profile. The devil is in the details!
Nothing so complicated, the whole thing is done in a matter of seconds.
Knowing the number 4 gray patch is supposed to read 48%, that gives you a good start, right? Then you have basic exposure set. Then you adjust contrast by checking the other gray patches.
How "accurate" you can get in art reproduction is an old discussion that never gets resolved. My own position, based on fifteen years working as photographer in an art museum, is that even if you managed to get a full colorimetric match, it wouldn't look good. You can't simply reproduce, you always have to recreate to a certain extent.
When you hit the sweet spot, you have an equivalent version that will be accepted as accurate. You always need to compensate for the medium and a lot of other factors. Ultimately it always comes down to a pair of good eyes and good judgement.
But the colorchecker kicks it all off, and gives me a starting point and a reference while working.
If you took a raw close-up photo of the color checker chart, you will find the method to create a camera profile (using the free Adobe DNG Editor software) within this document-
Profile Your Camera With Adobe DNG Editor
This camera profile created and used in Lightroom will show the colors in your photos close to reality and also,
A photo that includes the color chart, taken in the same light as the subject in the gallery, will give a grey patch you can use to set the White Balance of all photos taken on the shoot. (As might the white wall)