We present the data reduction pipeline, MEAD, for Arizona Lenslets for Exoplanet Spectroscopy (ALES), the first thermal infrared integral field spectrograph designed for high-contrast imaging. ALES is an upgrade of LMIRCam, the 1 - 5 μm imaging camera for the Large Binocular Telescope, capable of observing astronomical objects in the thermal infrared (3 - 5 μm) to produce simultaneous spatial and spectral data cubes. The pipeline is currently designed to perform L-band (2.8 - 4.2 μm) data cube reconstruction, relying on methods used extensively by current near-infrared integral field spectrographs. ALES data cube reconstruction on each spectra uses an optimal extraction method. The calibration unit comprises a thermal infrared source, a monochromator and an optical diffuser designed to inject specific wavelengths of light into LBTI to evenly illuminate the pupil plane and ALES lenslet array with monochromatic light. Not only does the calibration unit facilitate wavelength calibration for ALES and LBTI, but it also provides images of monochromatic point spread functions (PSFs). A linear combination of these monochromatic PSFs can be optimized to fit each spectrum in the least-square sense via x2 fitting.