This frequently comes up in photographic reproduction jobs where one is trying to closely approximate some other object such as a painting antique drawing. This cannot be done with typical photographs even when adjusting them to a specific, matching, LAB color. Regular photographs increase color saturation and tailor contrast, boosting the midranges and decreasing highlight contrast. This process is called "Output Referred" and most of it occurs with the image is captured and converted to a jpeg, or when a RAW image is processed by a RAW convertor. This is done to produce pleasing images, not accurate images.
Accurate photography and reproduction is a process called "Scene Referred" and it involves controlled illumination with light that is reasonably close to D50 (roughly afternoon daylight and close to that of a 5,000K black body). Strobes are often surprisingly close to D50.
An example of where this is done is to capture, process, and print a photo of a photo. Then, when they are placed side by side under the same lighting, they should closely match.
To photograph images "accurately" one wishes to capture an image that can be converted to exactly match the colors reflected with the only modification to shift the white point to D50's white point and adjust the overall gain so that the captured LAB in the image is the same as the measured reflectance LAB (which will be D50 based). Doing this precisely is not possible as the camera color filters would have to meet The Luther/Ives criteria as well as initially illuminating the photographed object with D50. However, one can come very close using tools with scene referred rendering capability. Far, far closer than just tweaking a regular photograph.
First, you need a RAW capture. Then it should be processed using a camera profile created for scene referred rendering. Freeware, DCamProf, can do this and you can get source/docs/executables here for making Photoshop ACR compatible camera profiles:
Once you have this, you just adjust the Exposure, Temp., and Tint sliders so that the color of the reference point in the photograph matches your LAB measured (or known, say from a Colorchecker card). Don't adjust any other sliders. - This is for old CS3 vintage Photoshop. see instructions at the end of this post for Photoshop CC
You may need to do conversions from whatever Colorspace you use (I suggest Adobe RGB or ProPhoto RGB). Bruce Lindbloom has a convenient calculator for doing this.
After you have a scene referred photograph, you can print it retaining accurate color by selecting "Absolute Colorimetric Intent" which preserves colors. That is, if a color reads LAB (70,20,25) in Photoshop it should print the same and read close to that same LAB value. Most inkjets with 8 or more ink colors are capable of doing so quite precisely though they may require something called a custom profile.
Finally, always do a process crosscheck. Take a picture of a ColorChecker card then make your reproduction. They should match extremely closely aside from things like specular reflections if using glossy paper. Matte paper is preferable for tasks like these.
One last consideration. Avoid papers that have optical brighteners. These are used to make paper's look whiter by converting uV into bluish light. The problem is that you get considerable color shift depending on how much uV is in the light. It also tends to yellow within a relatively small number of years.
Process for scene referred imaging in Photoshop CC with ACR using a camera DCP "linear" profile:
ACR has changed over the years. For Photoshop CC the some ACR settings need to be adjusted per "madmanchan" on the Adobe Forums. He's an Adobe dev employee and general expert on color management.
For scene referred image processing, select the "Version 1 (2003) or Version 2 (2010) workflow available under the "camera" icon and the DCP profile. Then, in the main tab (left most "iris" icon) set the "Brightness" at 50 and the "Contrast" at 25. One can also move the "Black" in slightly to mitigate glare but it should be a fairly tiny amount. Other sliders at 0.
Adobe's processing is, to say the least, opaque, but this has produced good results for me allowing imaging of a colorchecker with an average dE2000 of 2 and max of 5. It's about 3 or 4 times better than just setting the white point and the L*50 patch.
Beyond this, the program "dcraw" has specific options for linear processing.