A measurement of the shape of the differential decay rate and the associated Isgur-Wise function for the decay ${\mathrm{\ensuremath{\Lambda}}}_{b}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ is reported, using data corresponding to $3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected with the LHCb detector in proton-proton collisions. The ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}(+\mathrm{anything})$ final states are reconstructed through the detection of a muon and a ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}$ baryon decaying into $p{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$, and the decays ${\mathrm{\ensuremath{\Lambda}}}_{b}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ are used to determine contributions from ${\mathrm{\ensuremath{\Lambda}}}_{b}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{*+}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ decays. The measured dependence of the differential decay rate upon the squared four-momentum transfer between the heavy baryons, ${q}^{2}$, is compared with expectations from heavy-quark effective theory and from unquenched lattice QCD predictions.