We benefit from the lattice QCD determination by the HPQCD of the Standard Model (SM) form factors for the B¯→D [Phys. Rev. D101 (2020) 074513] and the SM and tensor ones for the B¯→D (arXiv:2304.03137 [hep-lat]) semileptonic decays, and the heavy quark effective theory (HQET) relations for the analogous B → D decays obtained by F.U. Bernlochner et al. in Phys. Rev. D95 (2017) 115008, to extract the leading and sub-leading Isgur-Wise functions for the B¯→D decays. Further use of the HQET relations allows us to evaluate the corresponding scalar, pseudoscalar and tensor form factors needed for a phenomenological study of new physics (NP) effects on the B¯→D semileptonic decay. At present, the experimental values for the ratios RD=ΓB¯→Dτν¯/ΓB¯→Deμν¯ are the best signal in favor of lepton flavor universality violation (LFUV) seen in charged current (CC) b → c decays. In this work we conduct a study of NP effects on the B¯→Dτν¯ semileptonic decays by comparing tau spin, angular and spin-angular asymmetry distributions obtained within the SM and three different NP scenarios. As expected from SU(3) light-flavor symmetry, we get results close to the ones found in a similar analysis of the B¯→D case. The measurement of the B¯→Dℓν¯ semileptonic decays, which is within reach of present experiments, could then be of relevance in helping to establish or rule out LFUV in CC b → c transitions.