  A search is performed for the charmless three-body decays of the
$\Lambda_b^0$ and $\Xi_b^0$ baryons to the final states $\Lambda h^+h^{\prime
-}$, where $h^{(\prime)} = \pi$ or $K$. The analysis is based on a data sample,
corresponding to an integrated luminosity of $3 \rm fb^{-1}$ of $pp$
collisions, collected by the LHCb experiment. The $\Lambda_b^0 \to \Lambda
K^+\pi^-$ and $\Lambda_b^0 \to \Lambda K^+K^-$ decays are observed for the
first time and their branching fractions and $CP$ asymmetry parameters are
measured. Evidence is seen for the $\Lambda_b^0 \to \Lambda \pi^+\pi^-$ decay
and limits are set on the branching fractions of $\Xi_b^0$ baryon decays to the
$\Lambda h^+h^{\prime -}$ final states.
