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We investigate for the first time a certain class of non-factorisablecontributions of the four-quark operators ${\cal O}_{3-6}$ in the weakeffective Hamiltonian to the $\Lambda_b \to \Lambda \ell^+\ell^-$ decayamplitude. We focus on the case where a virtual photon is radiated from one ofthe light constituents of the $\Lambda_b$ baryon, in the kinematic situation oflarge hadronic recoil with an energetic $\Lambda$ baryon in the final state.The effect on the suitably defined ``non-local form factors'' is calculatedusing the light-cone sum rule approach for a correlator with an interpolatingcurrent for the light $\Lambda$ baryon. We find that this approach requires theintroduction of new soft functions that generalise the standard light-conedistribution amplitudes (LCDAs) for the heavy $\Lambda_b$ baryon. We give aheuristic discussion of their properties and a model that relates them to thestandard LCDAs. Within this framework, we provide numerical results for thesize of the non-local form factors considered.

Non-factorisable Contributions of Strong-Penguin Operators in $\Lambda_b \to \Lambda \ell^+\ell^-$ Decays