  In light of recent measurements suggesting potential lepton flavor
universality violations in semileptonic decays at collider experiments, this
article provides a concise study of tree- and loop-level $B$-hadron
semileptonic decays, $b \to c l \nu_l$ and $b \to s l^+ l^-$. We provide
predictions for lepton flavor violating observables, $\mathcal{R}_{J/\psi}$ and
$\mathcal{R}_{\eta_c}$, across the entire $q^2$ range. Our study employs the
Relativistic Independent Quark Model (RIQM), highlighting a model-dependent
approach to these observables. We compare our model's predictions with existing
lattice predictions, demonstrating the strong applicability of the RIQM
framework in describing $B_c$ decays. Additionally, we reassess global averages
for $\mathcal{R}_{D(D^*)}$ and $\mathcal{R}_{K(K^*)}$ in semileptonic
transitions. With the upcoming experimental upgrades and the anticipated Run 3
data on $B_c$ meson decays, rapid confirmation of these quantities could
indicate significant evidence of physics beyond the Standard Model, thereby
opening new pathways for understanding the complex flavor dynamics in $B$ meson
decays.
