Abstract: The differential branching fraction of the rare decay Lambda(0)(b) -> 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 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 GeV2/c(4) the differential branching fraction is measured as dB(Lambda(0)(b) -> Lambda mu(+)mu(-))/dq(2) = (1.18(-0.08)(+0.09) +/- 0.03 +/- 0.27) x 10(-7) (GeV2/c(4))(-1) where the uncertainties are statistical, systematic and due to the normalisation mode Lambda(0)(b) -> 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(FB)(l)) and hadron (A(FB)(h)) systems are measured for the first time. In the range 15 < q(2) < 20GeV(2)/c(4) they are found to be A(FB)(l) = -0.05 +/- 0.09 (stat) +/- 0.03 (syst) and A(FB)(h) = -0.29 +/- 0.07 (stat) +/- 0.03 (syst).