A proton-proton collision data sample, corresponding to an integrated luminosity of $3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected by LHCb at $\sqrt{s}=7$ and 8 TeV, is used to reconstruct $63\ifmmode\pm\else\textpm\fi{}9$ ${\mathrm{\ensuremath{\Omega}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Omega}}}_{c}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${\mathrm{\ensuremath{\Omega}}}_{c}^{0}\ensuremath{\rightarrow}p{K}^{\ensuremath{-}}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ decays. Using the ${\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}\ensuremath{\rightarrow}p{K}^{\ensuremath{-}}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ decay mode for calibration, the lifetime ratio and the absolute lifetime of the ${\mathrm{\ensuremath{\Omega}}}_{b}^{\ensuremath{-}}$ baryon are measured to be ${\ensuremath{\tau}}_{{\mathrm{\ensuremath{\Omega}}}_{b}^{\ensuremath{-}}}/{\ensuremath{\tau}}_{{\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}}=1.11\ifmmode\pm\else\textpm\fi{}0.16\ifmmode\pm\else\textpm\fi{}0.03$, ${\ensuremath{\tau}}_{{\mathrm{\ensuremath{\Omega}}}_{b}^{\ensuremath{-}}}=1.78\ifmmode\pm\else\textpm\fi{}0.26\ifmmode\pm\else\textpm\fi{}0.05\ifmmode\pm\else\textpm\fi{}0.06\text{ }\text{ }\mathrm{ps}$, where the uncertainties are statistical, systematic and from the calibration mode (for ${\ensuremath{\tau}}_{{\mathrm{\ensuremath{\Omega}}}_{b}^{\ensuremath{-}}}$ only). A measurement is also made of the mass difference, ${m}_{{\mathrm{\ensuremath{\Omega}}}_{b}^{\ensuremath{-}}}\ensuremath{-}{m}_{{\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}}$, and the corresponding ${\mathrm{\ensuremath{\Omega}}}_{b}^{\ensuremath{-}}$ mass, which yields ${m}_{{\mathrm{\ensuremath{\Omega}}}_{b}^{\ensuremath{-}}}\ensuremath{-}{m}_{{\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}}=247.4\ifmmode\pm\else\textpm\fi{}3.2\ifmmode\pm\else\textpm\fi{}0.5\text{ }\text{ }\mathrm{MeV}/{c}^{2}$, ${m}_{{\mathrm{\ensuremath{\Omega}}}_{b}^{\ensuremath{-}}}=6045.1\ifmmode\pm\else\textpm\fi{}3.2\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\pm\else\textpm\fi{}0.6\text{ }\text{ }\mathrm{MeV}/{c}^{2}$. These results are consistent with previous measurements.