  The differential branching fraction of the rare decay $\Lambda^{0}_{b}
\rightarrow \Lambda \mu^+\mu^-$ is measured as a function of $q^{2}$, the
square of the dimuon invariant mass. The analysis is performed using
proton-proton collision data, corresponding to an integrated luminosity of $3.0
\mbox{ fb}^{-1}$, collected by the LHCb experiment. Evidence of signal is
observed in the $q^2$ region below the square of the $J/\psi$ mass. Integrating
over $15 < q^{2} < 20 \mbox{ GeV}^2/c^4$ the branching fraction is measured as
$d\mathcal{B}(\Lambda^{0}_{b} \rightarrow \Lambda \mu^+\mu^-)/dq^2 = (1.18 ^{+
0.09} _{-0.08} \pm 0.03 \pm 0.27) \times 10^{-7} ( \mbox{GeV}^{2}/c^{4})^{-1}$,
where the uncertainties are statistical, systematic and due to the
normalisation mode, $\Lambda^{0}_{b} \rightarrow J/\psi \Lambda$, respectively.
In the $q^2$ intervals where the signal is observed, angular distributions are
studied and the forward-backward asymmetries in the dimuon ($A^{l}_{\rm FB}$)
and hadron ($A^{h}_{\rm FB}$) systems are measured for the first time. In the
range $15 < q^2 < 20 \mbox{ GeV}^2/c^4$ they are found to be $A^{l}_{\rm FB} =
-0.05 \pm 0.09 \mbox{ (stat)} \pm 0.03 \mbox{ (syst)}$ and $A^{h}_{\rm FB} =
-0.29 \pm 0.07 \mbox{ (stat)} \pm 0.03 \mbox{ (syst)}$.
