A search is performed for the as yet unobserved baryonic $Lambda_b rightarrow Lambda eta^prime$ and $Lambda_b rightarrow Lambda eta$ decays with 3$fb^{-1}$ of proton-proton collision data recorded by the LHCb experiment. The $B^0 rightarrow K_S^0 eta^prime$ decay is used as a normalisation channel. No significant signal is observed for the $Lambda_b rightarrow Lambda eta^prime$ decay. An upper limit is found on the branching fraction of $mathcal{B}(Lambda_b rightarrow Lambda eta^prime)<3.1times10^{-6}$} at 90% confidence level. Evidence is seen for the presence of the $Lambda_b rightarrow Lambda eta$ decay at the level of $3sigma$ significance, with a branching fraction $mathcal{B}(Lambda_b rightarrow Lambda eta)=(9.3^{+7.3}_{-5.3})times10^{-6}$}.