The prompt production of Λ c + baryons is studied in proton-lead collisions collected with the LHCb detector at the LHC. The data sample corresponds to an integrated luminosity of 1.58 nb−1 recorded at a nucleon-nucleon centre-of-mass energy of sNN−−−√=5.02sNN=5.02 TeV. Measurements of the differential cross-section and the forwardbackward production ratio are reported for Λ c +baryons with transverse momenta in the range 2 < pT < 10 GeV/c and rapidities in the ranges 1.5 < y∗ < 4.0 and −4.5 < y∗ < −2.5 in the nucleon-nucleon centre-of-mass system. The ratio of cross-sections of Λ c + baryons and D0 mesons is also reported. The results are compared with next-to-leading order calculations that use nuclear parton distribution functions.