You can do the mapping by using cvLUT or cv::LUT (C/C++)

http://docs.opencv.org/modules/core/doc/operations_on_arrays.html?highlight=lut#lut

Calling the function is trivial and is explained in the documentation.

try

unsigned short* p = (unsigned short*) lookUpTable.data;

You should simply pass an std::vector<char> with 256 elements as the lut parameter. Element with index i in this vector will specify the output value for all pixels with value i.

For instance, if you want to threshold the image at 80 (everything above or equal 80 becomes fully white and everything else becomes fully black), you could write something like this:

std::vector<char> lut(256);
for (int i = 0; i < 256; ++i) {
    lut[i] = i >= 80 ? 255 : 0;
}

cv::LUT(src, lut, dst);

Thanks to @Dan Mašek's comment above. I'm adding it as answer here so the question can be marked answered.

For a 3 channel lookup table, the input also needs to be 3 channel. Just merge 3 copies of the L channel back into a 3 channel Mat, and apply the LUT to the result.

Updated code:

void MainWindow::convertLightToDarkColorMap(const cv::Mat inputMat)
{
    // Create lookup table (LUT)

    cv::Mat lookupTable(1, 256, CV_8UC(3));
    for (int i=0; i<256; i++)
    {
        lookupTable.at<cv::Vec3b>(i)[0]= 255-i; // first channel  (B)
        lookupTable.at<cv::Vec3b>(i)[1]= 0;     // second channel (G)
        lookupTable.at<cv::Vec3b>(i)[2]= 255+i; // ...            (R)
    }

    // Convert to LAB color space.
    cv::Mat convertedLAB;
    cv::cvtColor(inputMat, convertedLAB, CV_BGR2Lab);

    // Isolate the L, A, B channels.
    cv::Mat convertedLABSplit[3];
    cv::split(convertedLAB, convertedLABSplit);

    // 3 channel LUT only works on a 3 channel input.  So take (3) copes of the L channel and merge them into one.
    cv::Mat trippleL;
    std::vector<cv::Mat> trippleLArr;
    trippleLArr.push_back(convertedLABSplit[0]);
    trippleLArr.push_back(convertedLABSplit[0]);
    trippleLArr.push_back(convertedLABSplit[0]);
    cv::merge( trippleLArr, trippleL);

    // Apply our custom lookup table to L channel.
    cv::Mat outputMat(inputMat.rows, inputMat.cols, CV_8UC3);
    cv::LUT(trippleL, lookupTable, outputMat);

    // Show the output image
    cv::imshow("Output", outputMat);
}