A measurement of the production of prompt $\Lambda_{\rm {c}}^{+}$ baryons in Pb-Pb collisions at $\sqrt{s_{\rm {NN}}} = 5.02$ TeV with the ALICE detector at the LHC is reported. The $\Lambda_{\rm {c}}^{+}$ and $\Lambda_{\rm {c}}^{-}$ were reconstructed at midrapidity ($|y| < 0.5$) via the hadronic decay channel $\Lambda_{\rm {c}}^{+} \to {\rm {p}} {\rm {K}}^{0}_{\rm {S}}$ (and charge conjugate) in the transverse momentum and centrality intervals 6 < $p_{\rm {T}}$ <12 GeV/${\it {c}}$ and 0-80%. The $\Lambda_{\rm {c}}^{+}$/${\rm D}^{0}$ 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 $\sqrt{s_{\rm {NN}}} = 5.02$ 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. The $\Lambda_{\rm {c}}^{+}$/${\rm D}^{0}$ 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 $\Lambda_{\rm {c}}^{+}$ nuclear modification factor, $R_\mathrm{AA}$, is also presented. The measured values of the $R_\mathrm{AA}$ of $\Lambda_{\rm {c}}^{+}$, ${\rm D}_{\rm {s}}$ and non-strange D mesons are compatible within the combined statistical and systematic uncertainties. They show, however, a hint of a hierarchy $R_\mathrm{AA}^{{\rm D}^{0}}<R_\mathrm{AA}^{{\rm D}_{\rm {s}}}<R_\mathrm{AA}^{\Lambda_{\rm {c}}^{+}}$, conceivable with a contribution of recombination mechanisms to charm hadron formation in the medium.