Very-high-energy (VHE; 50 GeV < E < 100 TeV) gamma-ray telescopes observe cosmic particle accelerators, probing fundamental acceleration processes at energies far beyond those achievable at terrestrial accelerators and in extreme environments such as supernova remnants, pulsars, pulsar winds, and the Galactic Center. The upgraded H.E.S.S.-II telescope array saw first light in July 2012 and represents the cutting edge of the imaging atmospheric Cherenkov technique that enables observations of VHE gamma rays from ground-based facilities. This project will take advantage of the new data from H.E.S.S.-II, now the largest such telescope, with an unprecedented sensitivity to gamma-rays, in particular at low energies (50 < E < 150 GeV) which were previously beyond reach. Access to this key energy range will allow us to search for pulsed VHE emission from energetic pulsars, such as that unexpectedly observed from the Crab pulsar in 2011. It will also permit us to investigate the very recent yet mounting evidence for gamma-ray spectral lines from the Galactic Center and unassociated sources seen by the Fermi Gamma-ray Space Telescope. Utilizing an inter-disciplinary approach, we will integrate a monitoring LIDAR system with H.E.S.S.-II to directly calibrate the telescope data using grid-produced Monte Carlo simulations based on real-time, measured atmospheric properties. The implementation of an atmospheric monitoring and calibration program for H.E.S.S.-II and the next-generation Cherenkov Telescope Array is expected to improve energy resolution, reduce spectral bias, and minimize systematic uncertainties. The improvements provided by this project aim not only to address our specific research questions but also to provide, for the first time, the precision VHE gamma-ray spectroscopy required to further elucidate the underlying mechanisms responsible for gamma-ray production in the cosmos.