The lunar surface represents a complex plasma environment due to the presence of solar ultraviolet (UV) radiation, the incoming solar wind flux and charged, levitated micron- and sub-micron sized dust particles. Photoemission due to solar UV radiation dominates the charging environment, creating a photoelectron sheath above the lunar surface. To further investigate the dusty plasma environment on the surface of the Moon, a one-dimensional particle-in-cell (PIC) code has been designed specifically for the lunar surface. The code has been validated against analytic solutions for photoelectron sheaths with basic photoelectron energy distributions. Simulations have focused on the role of the emitted photoelectron energy distribution and solar UV variability in determining the sheath profile. Additionally, the charging and levitation of test dust particles in the photoelectron sheath are studied. Limits on the maximum size and height of levitated dust grains are also presented.