The QCD description of exclusive decays of the Lambda(b) baryon involves hadronic matrix elements of non-local light ray operators, the light-cone distribution amplitudes. We introduce the complete set of three-quark distribution amplitudes and calculate the renormalization scale dependence for the leading twist. At leading order in the strong coupling the evolution is driven by pairwise two-quark interactions: heavy-light involving Sudakov logarithms as in the B-meson case, and light-light as in light mesons. We solve the evolution equation and show that its main effect is to generate a radiative tail extending to high energies. Finally, we present simple models for the distribution amplitudes based on QCD sum rules, and study the effect of the evolution on these models. (C) 2008 Elsevier B.V. All rights reserved.