In this work we analyze cLFV processes using a low-energy EFT that induces the effective interaction between two charged leptons of different flavor and two photons. We compute ℓi → ℓjγ, ℓi → ℓjγγ decays and ℓi → ℓj conversion in nuclei. We derived indirect upper limits on the double photon decays, which turned out to be below current experimental bounds. Our prediction for ℓ → τ conversion in nuclei is below the expected sensitivity of the NA64 experiment