  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 $\mathcal{B}(\Lambda_b \rightarrow \Lambda
\eta^\prime)<3.1\times10^{-6}$} at 90\% confidence level. Evidence is seen for
the presence of the $\Lambda_b \rightarrow \Lambda \eta$ decay at the level of
$3\sigma$ significance, with a branching fraction $\mathcal{B}(\Lambda_b
\rightarrow \Lambda \eta)=(9.3^{+7.3}_{-5.3})\times10^{-6}$}.
