Decays of Ξb− and Ωb− baryons to Λc+h−h′− final states, with h−h′− being π−π−, K−π− and K−K− meson pairs, are searched for using data collected with the LHCb detector. The data sample studied corresponds to an integrated luminosity of 8.7 fb−1 of pp collisions collected at centre-of-mass energies s = 7, 8 and 13 TeV. The products of the relative branching fractions and fragmentation fractions for each signal mode, relative to the B−→Λc+p¯π− mode, are measured, with Ξb−→Λc+K−π−, Ξb−→Λc+K−K− and Ωb−→Λc+K−K− decays being observed at over 5 σ significance. The Ξb−→Λc+K−π− mode is also used to measure the Ξb− production asymmetry, which is found to be consistent with zero. In addition, the B−→Λc+p¯K− decay is observed for the first time, and its branching fraction is measured relative to that of the B−→Λc+p¯π− mode.