We have characterized the physical properties (electron temperature, density and metallicity) of the ionized gas and the ionizing population (age, metallicity and presence of Wolf-Rayet stars) in the Lynx arc, an HII galaxy at z= 3.36. The ultraviolet doublets (i.e. CIII], SiIII] and NIV) imply the existence of a density gradient in this object, with a high-density region (0.1-1.0 × 105cm-3) and a lower density region (<3200cm-3). The temperature-sensitive ratio [OIII]λλ1661,1666/λ5007 implies an electron temperature Te= 17300+500-700 K, in agreement within the errors with photoionization model predictions. Nebular abundance determination using standard techniques and the results from photoionization models imply a nebular metallicity of O/H ~ 10 +/- 3percent (O/H)solar, in good agreement with recent results from Fosbury et al. Both methods suggest that nitrogen is overabundant relative to other elements, with [N/O]~ 2.0-3.0 ×[N/O]solar. We do not find evidence for Si overabundance, as Fosbury et al. did. Photoionization models imply that the ionizing stellar population in the Lynx arc has an age of <~5 Myr. If He+ is ionized by Wolf-Rayet (WR) stars, then the ionizing stars in the Lynx arc have metallicities Zstar > 5percent Zsolar and ages ~2.8-3.4 Myr (depending on Zstar), when WR stars appear and are responsible for the He2+ emission. However, alternative excitation mechanisms for this species are not discarded. Since the emission lines trace the properties of the present burst only, nothing can be said about the possible presence of an underlying old stellar population. The Lynx arc is a low-metallicity HII galaxy that is undergoing a burst of star formation of <~5 Myr age. One possible scenario that explains the emission-line spectrum of the Lynx arc, the large strength of the nitrogen lines and the He2+ emission is that the object has experienced a merger event that has triggered a burst of star formation. WR stars have formed that contribute to a fast enrichment of the interstellar medium. Like Fosbury et al., we find a factor of >~10 discrepancy between the mass of the instantaneous burst required to power the luminosity of the Hβ line and the mass implied by the continuum level measured for the Lynx arc. We discuss several possible solutions to this problem. The most likely explanation is that gas and stars have different spatial distributions, so that the emission lines and the stellar continuum suffer different gravitational amplifications by the intervening cluster.