$B^+$, $B^0$, $B^0_s$, $\Lambda_B$ lifetimes and lifetime ratios.

We present new, high-statistics measurements of b hadron lifetimes from exclusive decays containing a $J/\psi$ selected using a dimuon trigger in CDF. The analysis uses about 800 pb$^{-1}$ of data from Run II of the Tevatron collider. In addition to the channels $B^+ \rightarrow J/\psi K^+$, $B^0 \rightarrow J/\psi K^{0*}$, $B^0\rightarrow J/\psi K^0_s$, which are well measured at B factories, we measure lifetimes of $\Lambda_b$ and $B_s^0$, (unique to the Tevatron) in the channels $B^0_s\rightarrow J/\psi\phi$ and $\Lambda_b \rightarrow J/\psi\Lambda^0$. Systematic errors in the ratios of lifetimes are minimized by the consistent use of the $J/\psi$ vertex across all decay channels, to estimate proper decay time.