The (x, y) position reconstruction method used in the analysis of the complete exposure of the Large Underground Xenon (LUX) experiment is presented. The algorithm is based on a statistical test that makes use of an iterative method to recover the photomultiplier tube (PMT) light response directly from the calibration data. The light response functions make use of a two dimensional functional form to account for the photons reflected on the inner walls of the detector. To increase the resolution for small pulses, a photon counting technique was employed to describe the response of the PMTs. The reconstruction was assessed with calibration data including 83mKr (releasing a total energy of 41.5 keV) and 3H (β− with Q = 18.6 keV) decays, and a deuterium-deuterium (D-D) neutron beam (2.45 MeV) . Within the detector's fiducial volume, the reconstruction has achieved an (x, y) position uncertainty of σ = 0.82 cm and σ = 0.17 cm for events of only 200 and 4,000 detected electroluminescence photons respectively. Such signals are associated with electron recoils of energies ~0.25 keV and ~10 keV, respectively. The reconstructed position of the smallest events with a single electron emitted from the liquid surface (22 detected photons) has a horizontal (x, y) uncertainty of 2.13 cm.