The LUX dark matter search experiment is a 350 kg dual-phase xenon time projection chamber located at the 4850 ft level of the Sanford Underground Research Facility in Lead, SD. The success of two-phase xenon detectors for dark matter searches relies on their ability to distinguish electron recoil (ER) background events from nuclear recoil (NR) signal events. Typically, the NR-ER discrimination is obtained from the ratio of the electroluminescence light (S2) to the prompt scintillation light (S1). Analysis of the S1 pulse shape is an additional discrimination technique that can be used to distinguish NR from ER. Pulse-shape NR-ER discrimination can be achieved based on the ratio of the de-excitation processes from singlet and triplet states that generate the S1. The NR S1 is dominated by the de-excitation process from singlet states with a time constant of about 3 ns while the ER S1 is dominated by the de-excitation process from triplet states with a time constant of about 24 ns. As the size of the detectors increases, the variation in the S1 photon flight path can become comparable to these decay constants, reducing the utility of pulse-shape analysis to separate NR from ER. The effect of path length variations in the LUX detector has been studied using the results of simulations and the impact on the S1 pulse shape analysis is discussed.