A measurement of the production of prompt ${\Lambda }_c^{+}$ baryons in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with the ALICE detector at the LHC is reported. The ${\Lambda }_c^{+}$ and ${{\bar{\Lambda }}_c}^{-}$ were reconstructed at midrapidity ($\left|y\right|<0.5$) via the hadronic decay channel ${\Lambda }_c^{+}\to p{K}_S^0$ (and charge conjugate) in the transverse momentum and centrality intervals $6<p_T<12$ GeV/c and 0–80%. The ${\Lambda }_c^{+}/D^0$ 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 $\sqrt{s}=7$ TeV and in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ 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 $p_T$ interval covered by the measurements in the two collision systems. The ${{\Lambda }_c}^{+}/D^0$ 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 ${\Lambda }_c^{+}$ nuclear modification factor, $R_{\mathrm{AA}}$, is also presented. The measured values of the $R_{\mathrm{AA}}$ of ${\Lambda }_c^{+}$, $D_s^{+}$ and non-strange D mesons are compatible within the combined statistical and systematic uncertainties. They show, however, a hint of a hierarchy $(R_{\mathrm{AA}}^{D^0}<R_{\mathrm{AA}}^{D_s^{+}}<R_{\mathrm{AA}}^{{\Lambda }_c^{+}})$, conceivable with a contribution from coalescence mechanisms to charm hadron formation in the medium.