Cuprous chalcogenide, Cu2Se, attracted attention due to its large Seebeck coefficient coupled with low thermal conductivity, facilitated by the presence of disordered Cu-ions in the structure of Cu-Se. This compound is thermally unstable prompting investigation of its analogue Cu2Te which has a lower figure-of-merit zT due to its high charge carrier concentration. In the present work, a dual substitution, both cation and anion by Li and Se, respectively, has been attempted to enhance zT. The Cu2-xLixTe1-ySey alloys have been synthesized by a simple, conventional arc melting process and investigated without subjecting to any further processing. The room temperature microstructure shows a plate-like layered nanostructure in the grains with the grains oriented in random directions. The alloys at room temperature have two polymorphic phases, superstructured hexagonal and orthorhombic, co-existing in all the alloys. The alloys exhibit a degenerate semiconducting behavior in the range 300-1000 K with the conductivity decreasing from similar to 3000 Scm(-1) to 700 Scm(-1). All the alloys show a hole dominant Seebeck coefficient which increases with temperature from similar to 30 to 135 mu VK-1. The alloy with dual substitution, Li-0.1 and Se-0.03, has the highest power factor of 1.6 mWm(-1) K-2 at 1000 K. It's low thermal conductivity in the complete range < 1.5 Wm(-1) K-1 results in increasing the zT to 1.0 at 1000 K, an increase of 130% compared to the undoped alloy. These alloys are found to be thermally and temporally stable with no significant power loss either due to thermal cycling or aging.