We explore the possibility of lepton number violation (LNV) manifesting in the rare kaon decay $K\to\pi\nu\nu$, its consequences for radiative neutrino mass generation and the washout of lepton asymmetry in high-scale leptogenesis scenarios. We perform the analysis in a model-independent framework, the Standard Model effective field theory (SMEFT). Possibilities to detect the LNV nature of the rare kaon decay are discussed in the context of the currently operating NA62 experiment at CERN and the KOTO experiment at J-PARC. We find that LNV could be detectable, and that any such detection would put high-scale leptogenesis under tension but could account for small radiatively generated neutrino masses.