Hi [USER=138320]@jmyers732003[/USER]
Some clarification and extra information would be helpful in giving good suggestions.
Note that ideally, if your work is fully color managed from you digital image, to your monitor, to your proof printer, or to the final printer, you should be able to create close to the exact color you desire on output from applying the desired color number in Photoshop. There are exceptions to this if you are printing to a printer whose paper and ink combination does not suport the desired color (e.g. it was out of gamut) and the rendering intent option shifts the color on printing (e.g. perceptual).
It would also be good to know the color mode and color spaces used for the entire workflow. You can used Lab color mode in Photoshop yet when printing almost all printers either need RGB or CMYK and an associated color profile with each. The chosen rendering intent make a difference as well.
Is the delta numbers comparing a reading off the customers sample compared to a local Epson print sample? What device is being used for the measurement?
Can you provided the actual measurement numbers for both as opposed to just the delta between the two. e.g. from just a delta number I don't know if the Lab numbers are higher of lower from the customer target print.
If we are not working with a complete color managed and calibrated workflow is one path and if we are just winging it to nudge color numbers close then that is a totally different approach (and harder because it could take some iterations)
Answering the above will make any suggestions I or other forum members make more on target for a better desired result.
Hope this will be a good start to resolution
John Wheeler