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In this paper, we studied the semileptonic decays $B_c^- \to (\eta_c, J/\psi)l ^- \bar{\nu}_l$ by employing the PQCD factorization approach, using the newlydefined distribution amplitudes of the $B_c$ meson and the new kind ofparametrization for extrapolation of the form factors , and also taking intoaccount the lattice QCD results about the relevant form factors at severalpoints. We found the following main results: (a) the PQCD predictions for thebranching ratios of $B_c \to (\eta_c,J/\psi) l \bar{\nu}$ decays will become alittle smaller by about $(5-16)\%$ when the lattice input are taken intoaccount in the extrapolation of the relevant form factors; (b) the PQCDpredictions for the ratio $R_{\eta_c, J/\psi}$ and the longitudinalpolarization $P_{\tau}$ are $R_{\eta_c}=0.34\pm 0.01 , R_{J/\psi}=0.28\pm0.01$, $P_{\tau}(\eta_c) = 0.37\pm 0.01$ and $P_{\tau}(J/\psi) = -0.55 \pm0.01$ ; and (c) after the inclusion of the lattice input the theoreticalpredictions changed slightly: $R_{\eta_c}=0.31\pm 0.01$, $ R_{ J/\psi}=0.27\pm0.01$, $P_{\tau}( \eta_c) = 0.36 \pm 0.01$ and $P_{\tau}( J/\psi) = -0.53\pm0.01$. The theoretical predictions for $R_{ J/\psi}$ agree with the measuredone within errors, and other predictions could be tested in the near futureLHCb experiments.

Semileptonic decays $B_c \to (\eta_c,J/\psi) l \bar{\nu}_l $ in the "PQCD + Lattice" approach