A measurement of the production of prompt Λc+ baryons in Pb–Pb collisions at √sNN=5.02 TeV with the ALICE detector at the LHC is reported. The Λc+ and Λ‾c− were reconstructed at midrapidity ( |y|<0.5 ) via the hadronic decay channel Λc+→pKS0 (and charge conjugate) in the transverse momentum and centrality intervals pT<6, 12> GeV/c and 0–80%. The Λc+/D0 ratio, which is sensitive to the charm quark hadronisation mechanisms in the medium, is measured and found to be larger than the ratio measured in minimum-bias pp collisions at √s=7 TeV and in p–Pb collisions at √sNN=5.02 TeV. In particular, the values in p–Pb and Pb–Pb collisions differ by about two standard deviations of the combined statistical and systematic uncertainties in the common pT interval covered by the measurements in the two collision systems. The Λc+/D0 ratio is also compared with model calculations including different implementations of charm quark hadronisation. The measured ratio is reproduced by models implementing a pure coalescence scenario, while adding a fragmentation contribution leads to an underestimation. The Λc+ nuclear modification factor, RAA , is also presented. The measured values of the RAA of Λc+ , Ds+ and non-strange D mesons are compatible within the combined statistical and systematic uncertainties. They show, however, a hint of a hierarchy (RAAD0 < RAADs+ < RAAΛc+) , conceivable with a contribution from coalescence mechanisms to charm hadron formation in the medium.