The decays Lambda(0)(b) -> psi(2S)pK(-) and Lambda(0)(b) -> J/psi pi(+)pi(-)pK(-) are observed in a data sample corresponding to an integrated luminosity of 3 fb(-1), collected in proton-proton collisions at 7 and 8 TeV centre-of-mass energies by the LHCb detector. The psi(2S) mesons are reconstructed through the decay modes psi(2S) -> mu(+)mu(-) and psi(2S) -> J/psi pi(+)pi(-) The branching fractions relative to that of Lambda(0)(b) -> J/psi pk(-) are measured to be [GRAPHICS] where the first uncertainties are statistical, the second are systematic and the third is related to the knowledge of J/psi and psi(2S) branching fractions. The mass of the Ai baryon is measured to be M(Lambda(0)(b)) = 5619.65 +/- 0.17 0.17 MeV/c(2), where the uncertainties are statistical and systematic.