  Lepton flavour violation (LFV) naturally occurs in many new physics models,
specifically in those explaining the $B$ anomalies. While LFV has already been
studied for mesonic decays, it is important to consider also baryonic decays
mediated by the same quark transition. In this paper, we study LFV in the
baryonic $\Lambda_b \to \Lambda \ell_1 \ell_2$ using for the first time a full
basis of New Physics operators. We present expected bounds on the branching
ratio in a model-independent framework and using two specific new physics
models. Finally, we point out the interplay and orthogonality between the
baryonic and mesonic LFV searches.
