The aim purpose of this work is to investigate the various physical properties of the new synthesized alkali-metal based Heusler alloy Li2CoSb using the density functional theory. The results showed that the compound has ferromagnetic ground state and is mechanically stable against any small deformations. We performed calculations for different exchange-correlation potentials to obtain the magneto-electronic properties. The generalized gradient approximation (GGA) findings showed a metallic electronic nature with a weak magnetic moment. However, calculations by the modified Becke–Johnson exchange potential combined with GGA correlation (mBJ-GGA) indicated an increase in the magnetic moment but the alloy remains with a metallic character. To respect the strong electron correlation effect for the localized d states in the calculations, the mBJ-GGA + U scheme was used. The Half-metallic ferromagnetism behavior with integer total magnetic moment was found. The half-metallic property is preserved at a range 2–5 eV of Hubbard U parameter. The thermoelectric properties were calculated and divulged that the compound studied exhibit a high figure of merit, large Seebeck coefficient, and low thermal conductivity. Hence, the Li2CoSb is a good thermoelectric compound. The thermal and pressure effect on the isochoric and isobaric heat capacity and Debye temperature were studied using the quasiharmonic approximation. It is important to emphasis that all the investigated properties have not been studied yet for the present Li-based Heusler compound. Therefore, the present work can be considered as a first report.