Currently, the formation of a two-dimensional electron gas (2DEG) at the TiO₂/LaO-terminated interface between LaAlO₃ (LAO) grown on SrTiO₃(001) (STO) is well understood. The role of the polarity of LAO and its critical thickness for the formation of 2DEG have been established. Here, we show how 2DEG can be tuned externally by changing electronic balance at the LAO(001) surface or, alternatively, at the intrinsically hole-doped AlO₂/SrO interface of LAO/STO heterostructures. The effects of liquid gating at LAO(001) and imperfected AlO₂/SrO were simulated in the framework of the first-principles Green function method within the coherent-potential approximation. We evaluated the Fermi surface cross sections, which were computed varying the degree of chemical disorder. These findings may be extremely important for potential application of 2DEG.