Lepton flavor universality can be tested through the ratio of semileptonic $B$ meson decays and leptonic $\Upsilon$ meson decays, with $\Upsilon \equiv \Upsilon(nS)$ ($n=1,2,3$). For the charged-current transitions $b \to c\tau\bar{\nu}_\tau$, discrepancies between the experiment and the Standard Model (SM) have been observed in recent years by different flavor facilities such as BABAR, Belle, and LHCb. While for the neutral-current transitions $b \bar{b} \to \tau\bar{\tau}$, the BABAR experiment reported recently a new measurement of leptonic decay ratio $R_{\Upsilon(3S)} = {\rm BR}(\Upsilon(3S) \to \tau^+\tau^-)/{\rm BR}(\Upsilon(3S) \to \mu^+\mu^-)$, showing an agreement with the SM at the $1.8 \sigma$ level. In light of this new BABAR result and regarding the connection between new physics (NP) interpretations to the charged-current $b \to c \tau \bar{\nu}_{\tau}$ anomalies and neutral-current $b \bar{b} \to \tau \bar{\tau}$ processes, in this study, we revisit the NP consequences of this measurement within a simplified model with extra massive gauge bosons that coupled predominantly to left-handed leptons of the third-generation. We show that the BABAR measurement of $R_{\Upsilon(3S)}$ cannot easily be accommodated (within its experimental $1\sigma$ range) together with the other $b \to c\tau\bar{\nu}_\tau$ data, hinting toward a new anomalous observable.