Lesinurad (systematic name: 2-{[5-bromo-4-(4-cyclopropylnaphthalen-1-yl)-4H-1,2,4-triazol-3-yl]sulfanyl}acetic acid, C17H14BrN3O2S) is a selective uric acid reabsorption inhibitor related to gout, which exhibits poor aqueous solubility. High-throughput solid-form screening was performed to screen for new solid forms with improved pharmaceutically relevant properties. During polymorph screening, we obtained two solvates with methanol (CH3OH) and ethanol (C2H5OH). Binary systems with caffeine (systematic name: 3,7-dihydro-1,3,7-trimethyl-1H-purine-2,6-dione, C8H10N4O2) and nicotinamide (C6H6N2O), polymorphs with urea (CH4N2O) and eutectics with similar drugs, like allopurinol and febuxostat, were prepared using the crystal engineering approach. All these novel solid forms were confirmed by XRD, DSC and FT-IR. The crystal structures were solved by single-crystal and powder X-ray diffraction. The crystal structures indicate that the lesinurad molecule is highly flexible and the triazole moiety, along with the rotatable thioacetic acid (side chain) and cyclopropane ring, is almost perpendicular to the planar naphthalene moiety. The carboxylic acid-triazole heterosynthon in the drug is interrupted by the presence of methanol and ethanol molecules in their crystal structures and forms intermolecular macrocyclic rings. The caffeine cocrystal maintains the consistency of the acid-triazole heterosynthons as in the drug and, in addition, they are bound by several auxiliary interactions. In the binary system of nicotinamide and urea, the acid-triazole heterosynthon is replaced by an acid-amide synthon. Among the urea cocrystal polymorphs, Form I (P-1, 1:1) consists of an acid-amide (urea) heterodimer, whereas in Form II (P21/c, 2:2), both acid-amide heterosynthons and urea-urea dimers co-exist. Density functional theory (DFT) calculations further support the experimentally observed synthon hierarchies in the cocrystals. Aqueous solubility experiments of lesinurad and its binary solids in pH 5 acetate buffer medium indicate the apparent solubility order lesinurad-urea Form I (43-fold) > lesinurad-caffeine (20-fold) > lesinurad-allopurinol (12-fold) ≃ lesinurad-nicotinamide (11-fold) > lesinurad, and this order is correlated with the crystal structures.