A search is performed for the as yet unobserved baryonic Lambda(0)(b) -> Lambda eta' and Lambda(0)(b) -> Lambda eta decays with 3 fb(-1) of proton-proton collision data recorded by the LHCb experiment. The B-0 -> K-s(0)eta' decay is used as a normalisation channel. No significant signal is observed for the Lambda(0)(b) -> Lambda eta' decay. An upper limit is found on the branching fraction of B(Lambda(0)(b) -> Lambda eta') < 3.1 x 10(-6) at 90% confidence level. Evidence is seen for the presence of the Lambda(0)(b) -> Lambda eta 0 decay at the level of 3 sigma significance, with a branching fraction B(Lambda(0)(b) -> Lambda eta) = (9.3(-5.3)(+7.3)) x 10(-6).