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During the accretion phase of a core-collapse supernova (SN), the deleptonization flux has recently been found to develop a global dipole pattern [lepton emission self-sustained asymmetry (LESA)]. The νe number flux Fνe is much larger than F¯νe in one direction, whereas they are approximately equal, or even Fνe≲ F¯νe , in the opposite direction. We use a linearized stability analysis in a simplified SN model to study the impact of the νe–¯νe flux asymmetry on self-induced neutrino flavor conversion. While a small lepton-number flux facilitates self-induced flavor conversion, “multiangle matter suppression” is more effective. Overall, we find that for large matter densities which are relevant below the shock wave, self-induced flavor conversion remains suppressed in the LESA context and, thus, irrelevant for neutrino-driven explosion dynamics.