Sounds a bit iffy to me... A card, by itself, DOESN'T have a fixed L*a*b* colour - that's a product of the reflectivity of the card at different wavelengths and the intensity and wavelength distribution of the illumination. In the dark, L* will be 0. Light it with a coloured light and your a*b* will change. Light it with a "white" light with a different wavelength distribution and your a*b* may change due to metamerism. Light it with a different colour temperature and things will change. Change the brightness of the illumination or the distance or angle of the card relative to the light source and your L* will change.

However, assuming you're taking the picture under the correct standard lighting that your original card L*a*b* values were measured under (Which may well be different from natural light or camera flash - commercial printing often uses D50), And assuming that what you're interested in falls in the linear portion of the sensor response in all channels (anti blooming sensors start discarding some of the charge as the pixel well fills up), then you can probably get away with tweaking the exposure level to get the card to match your desired L* values. But be aware that even if you're using standard lighting, your L* value will vary based on distance and angle to the light source - and both brightness and colour may vary due to additional light reflected onto that part of the scene from surrounding objects.

But the usual way of measuring colours when accuracy is important is to use something called a spectrophotometer - these are usually contact (or near contact) instruments that measure the reflectivity of the target patch across a whole range of wavelengths, which also allows them to calculate accurate XYZ colour values, rather than trying to work out an accurate colour from RGB filtered samples alone, which don't always get it right (as anyone who has tried photographing bluebells will probably have noticed). This is why professionally generated ICC colour profiles normally use a spectrophotometer to meaure printed colour patches.

Which isn't to say you can't do useful things from a photo - you just have to be aware of the issues and limitations.