The quaternary Heusler alloys with composition LiAEFeSb have been studied in this manuscript (AE = Alkaline Earth elements Be, Mg, Ca, Sr and Ba) for their potential applications in spintronics. All the investigations have been performed by employing density functional theory. A systematic comparison of results obtained within local density approximation (LDA) and the generalized gradient approximation (GGA) done. Our calculations reveal that all the studied alloys have lowest energy in type-I arrangement of basis and exhibit interesting electronic and magnetic properties. All the alloys exhibit a stable ferromagnetic ground state. Fixed spin moment calculations rule out existence of any other local magnetic minima. The phonon dispersions show that all the alloys except LiBeFeSb are dynamically stable. Notably, LiSrFeSb and LiBaFeSb exhibit half-metallic electronic band structure and 100 % spin polarization making them suitable choice for promising spintronic applications such as spin filter and detectors.