We have studied the desorption of positive ions from a LiF(110) crystal surface using positron and electron irradiation at 500 eV to examine the interaction between positrons and ionic crystals. Only monatomic ions, such as H^{+}, Li^{+}, and F^{+}, are detected under electron irradiation. However, positron irradiation leads to the significant desorption of ionic molecules, specifically, FH^{+} and F_{2}^{+}. Molecular ion yields are more sensitive to temperature than atomic ion yields. Based on the findings, we propose a desorption model in which positronic compounds are initially produced at the surface and subsequently desorbed as molecular ions via Auger decay following positron annihilation.