  In light of prospects for measurements of $B_c \rightarrow D^{(\ast)} l \nu$
decays in the upcoming Upgrade II of the LHC, we show that by using calculated
$B_c \rightarrow D^{(\ast)}$ form factors competitive extraction of the
$|V_{ub}|$ CKM matrix element from the $B_c \to D \mu \bar{\nu}_{\mu}$ decay
might be possible. To minimize experimental and theoretical uncertainties we
provide the ratio $|V_{ub}|/|V_{cb}|$ by normalizing the $B_c \rightarrow
D^{(\ast)} \mu \bar{\nu}_{\mu}$ to $B_c \to J/\psi \mu \bar{\nu}_{\mu}$ decay.
We also briefly examine the suggestion to extract $|V_{ub}|/|V_{cs}|$ from the
theoretically interesting ratio of $B_c \rightarrow D^0 e \bar{\nu}_{e}$ and
$B_c \rightarrow B_s e \bar{\nu}_{e}$ decay rates in the zero-recoil limit.
With the present average value of $|V_{ub}|$, the predicted branching ratios
are estimated to be $BR(B_c \to D^0 \mu \bar{\nu}_{\mu}) = (2.4\pm 0.4)\cdot
10^{-5} $ and $BR(B_c \to D^{\ast} \mu \bar{\nu}_{\mu}) = (7\pm3)\cdot 10^{-5}
$, and the semileptonic ratios for testing the lepton flavour universality in
these $B_c$ decays are $R_c(D^0) =0.64 \pm 0.05$ and $R_c(D^{\ast}) = 0.55 \pm
0.05$. We also provide $q^2$ distributions and various angular observables of
$B_c \rightarrow D^{(\ast)} l \nu$ decays.
