We calculate permanent electric dipole moments (PDMs), as well as spontaneous and black body lifetimes, of alkaline-earth-metal\char21{}Li (AEM-Li) ultracold polar molecules to study anisotropic long-range dipole-dipole interactions in a single quantum state. We obtain potential energy curves for the ${}^{2}\phantom{\rule{-0.16em}{0ex}}$Σ${}$ ground state of MgLi, CaLi, SrLi, and BaLi molecules at the coupled cluster singles and doubles with partial triples [CCSD(T)] level of electron correlation. Calculated spectroscopic constants for the isotopes: ${}^{24}$Mg${}^{7}$Li, ${}^{40}$Ca${}^{7}$Li, ${}^{88}$Sr${}^{7}$Li, and ${}^{138}$Ba${}^{7}$Li, show good agreement with available theoretical and experimental results. We obtain PDM curves using finite field perturbation theory at the CCSD(T) level. We find that AEM-Li molecules have moderate values of PDM at the equilibrium bond distance (MgLi: 0.90 D, CaLi: 1.15 D, SrLi: 0.33 D, and BaLi: \char21{}0.42 D) and hence might be suitable candidates for the proposed study in a single quantum state. Radiative lifetime calculations of the $$ν${}$ $=$ 0 state (${}^{24}$Mg${}^{6}$Li: 22 s, ${}^{40}$Ca${}^{6}$Li: 39 s, ${}^{88}$Sr${}^{6}$Li: 380 s, and ${}^{138}$Ba${}^{6}$Li: 988 s) are found to be longer than the typical time scale associated with ultracold experiments with these molecules. The uncertainty in the lifetime calculations are estimated to be less than 10$%$.