Prospective searches for lepton flavor violation (LFV) in rare kaon decays at the existing and future intermediate-energy accelerators are considered. The proposed studies are complementary to LFV searches in muon-decay experiments and offer a unique opportunity to probe models with approximately conserved fermion-generation quantum number with sensitivity superior to that in other processes. Consequently, new searches for LFV in kaon decays are an important and independent part of the general program of searches for lepton flavor violation in the final states with charged leptons.