Structures and properties of an Au₂₀ cluster doped with two Li atoms, Au₁₈L_i2, have been investigated using relativistic density functional theory within the framework of the zeroth-order regular approximation. Various initial structures have been generated and employed for geometry optimization followed by vibration analysis to check the stability of the final optimized structures. We have calculated various properties like binding energy, ionization potential, electron affinity and the HOMO–LUMO gap of these structures. It has been found that two dopant Li atoms favour occupying two different surface positions of the pyramidal Au₂₀ cluster. The binding energy of the surface-doped Au₁₈Li₂ cluster is 1.017 eV higher than that of the pure Au₂₀ cluster and the HOMO–LUMO gap (1.742 eV) is as high as a pure Au₂₀ cluster (1.786 eV). Interestingly, we observe that the HOMO–LUMO gap as well as the binding energy can be increased beyond those of the Au₁₈Li₂ cluster with the help of further Li atom doping. In fact, a doped tetrahedral Au₁₆Li₄ cluster, where all the dopants are at the surface sites, possesses a very high HOMO–LUMO gap of 2.117 eV. Geometric and energetic parameters indicate that the Au₁₆Li₄ cluster might be considered as a possible ‘superatom’ in the design of novel  cluster assembled materials.