  This paper presents updated measurements of the lifetimes of the B^0_s meson
and the \Lambda_b baryon using 4.4 million hadronic Z^0 decays recorded by the
OPAL detector at LEP from 1990 to 1995. A sample of B^0_s decays is obtained
using D_s^- \ell^+ combinations, where the D_s^- is fully reconstructed in the
\phi \pi^-, K^*0 K^- and K^- K^0_S decay channels and partially reconstructed
in the \phi \ell^- \nu(bar) X decay mode. A sample of \Lambda_b decays is
obtained using \Lambda_c^+ \ell^- combinations, where the \Lambda_c^+ is fully
reconstructed in its decay to a p K^- \pi^+ final state and partially
reconstructed in the \Lambda \ell^+ \nu X decay channel. From 172 +/- 28 D_s^-
\ell^+ combinations attributed to B^0_s decays, the measured lifetime is
  \tau(B^0_s) = 1.50 +0.16 -0.15 +/- 0.04 ps,
  where the errors are statistical and systematic, respectively. From the 129
+\- 25 \Lamda_c^+ \ell^- combinations attributed to \Lambda_b decays, the
measured lifetime
  \tau(\Lambda_b) = 1.29 +0.24 -0.22 +/- 0.06 ps,
  where the errors are statistical and systematic, respectively.
