  We investigate for the first time a certain class of non-factorisable
contributions of the four-quark operators ${\cal O}_{3-6}$ in the weak
effective Hamiltonian to the $\Lambda_b \to \Lambda \ell^+\ell^-$ decay
amplitude. We focus on the case where a virtual photon is radiated from one of
the light constituents of the $\Lambda_b$ baryon, in the kinematic situation of
large hadronic recoil with an energetic $\Lambda$ baryon in the final state.
The effect on the suitably defined ``non-local form factors'' is calculated
using the light-cone sum rule approach for a correlator with an interpolating
current for the light $\Lambda$ baryon. We find that this approach requires the
introduction of new soft functions that generalise the standard light-cone
distribution amplitudes (LCDAs) for the heavy $\Lambda_b$ baryon. We give a
heuristic discussion of their properties and a model that relates them to the
standard LCDAs. Within this framework, we provide numerical results for the
size of the non-local form factors considered.
