Lesinurad and allopurinol have been formulated in a combined dosage form providing a new challenge for the treatment of gout attacks. Two mathematical based spectrophotometric methods, area under the curve, and artificial neural networks have been developed for simultaneous determination of lesinurad and allopurinol in pure form and in combined pharmaceutical dosage form. Area under the curve has been utilized to resolve the spectral overlap between lesinurad and allopurinol. Values of area under the curve and area absorptivity were measured at two selected wavelength ranges of 242-250 nm and 255-265 nm. Two mathematically constructed equations have been used to determine the concentrations of the drugs under the study. Advanced chemometry based model, artificial neural network, has been developed utilizing the UV spectral data of lesinurad and allopurinol through various defined steps. A five-level, two-factor experimental design was used to construct 25 mixtures. Thirteen mixtures were used to set up the calibration model and 12 mixtures were used to construct a validation set. The artificial neural network model was optimized to enable precise spectrophotometric determination of the drugs under the study. The described mathematically bases spectrophotometric methods have been successfully applied to the determination of lesinurad and allopurinol in the new combined, Duzallo® tablets. Furthermore, the greenness of the described methods was assessed using four different tools namely, the national environmental method index, the analytical eco-scale, the green analytical procedure index and the AGREE evaluation method. The proposed methods showed more adherence to the greenness characters in comparison to the previously reported HPLC method.