Liquid Xenon (LXe) is an excellent material for experiments designed to detect dark matter in the form of Weakly Interacting Massive Particles (WIMPs). A low energy detection threshold is essential for a sensitive WIMP search. The understanding of the relative scintillation efficiency (Leff) and ionization yield of low energy nuclear recoils in LXe is limited for energies below 10 keV. In this paper, we present new measurements that extend the energy down to 4 keV, finding that Leff decreases with decreasing energy. We also measure the quenching of scintillation efficiency due to the electric field in LXe, finding no significant field dependence.