  The physics potential for $b$-baryon decays has been relatively unexplored
until the advent of the LHC, and as such important questions still exist about
their fundamental properties, such as whether their decays exhibit $C\!P$
violation. Presented here are observations of the decays $\Lambda_b^0
\rightarrow \Lambda K^+\pi^-$ and $\Lambda_b^0 \rightarrow \Lambda K^+K^-$,
made at a significance level of 8.1 and 15.8 Gaussian standard deviations,
respectively, and measurements of their branching fractions. The phase-space
integrated $C\!P$ asymmetries of these decays are also measured and found to be
consistent with zero. Limits are set on the branching fractions of other
$\Lambda_b^0$ and $\Xi_b^0$ decays to $\Lambda h^+h^{\prime -}$ (where $h$ is a
kaon or pion).
