A method for producing lithium hydroxide monohydrate from multicomponent lithium-bearing brines, the method including: (i) filtering the multicomponent lithium-bearing brine from solid-phase impurities to form a pregnant lithium-bearing brine, (ii) sorption separation of primary lithium concentrate from pregnant lithium-bearing brine in sorption-desorption columns with a fixed bed of a granular sorbent selective to LiCl in the form of an aqueous solution, (iii) decarbonizing the primary lithium concentrate by acidification, (iv) nanofiltration of the decarbonated primary lithium concentrate for non-reactive purification from magnesium, calcium and sulfate ions, (v) reverse osmosis concentration of the primary lithium concentrate purified by nanofiltration to obtain a permeate flow in the form of a demineralized aqueous solution and a reverse osmosis lithium chloride concentrate flow, (vi) concentration of the reverse osmosis lithium chloride concentrate by electrodialysis to obtain a lithium-containing dialysate flow and an electrodialyzed lithium chloride concentrate flow, (vii) chemical purification of the electrodialyzed lithium chloride concentrate from calcium, magnesium and sulfate ions, (viii) ion-exchange purification of the chemically purified electrodialyzed lithium chloride concentrate, (ix) boiling down the electrodialysis lithium chloride concentrate subjected to ion-exchange purification with salting out and separation of sodium chloride and potassium chloride crystals, (x) producing a pregnant lithium chloride solution by diluting the boiled-down lithium chloride concentrate with demineralized water, (xi) electrochemical conversion by membrane electrolysis of the pregnant lithium chloride solution to produce cathodic hydrogen, anodic chlorine, and an aqueous solution of lithium hydroxide as catholyte, (xii) boiling down the LiOH solution, (xiii) crystallization of LiOH·H 2 O from the boiled-down LiOH solution. (i) filtering the multicomponent lithium-bearing brine from solid-phase impurities to form a pregnant lithium-bearing brine, (ii) sorption separation of primary lithium concentrate from pregnant lithium-bearing brine in sorption-desorption columns with a fixed bed of a granular sorbent selective to LiCl in the form of an aqueous solution, (iii) decarbonizing the primary lithium concentrate by acidification, (iv) nanofiltration of the decarbonated primary lithium concentrate for non-reactive purification from magnesium, calcium and sulfate ions, (v) reverse osmosis concentration of the primary lithium concentrate purified by nanofiltration to obtain a permeate flow in the form of a demineralized aqueous solution and a reverse osmosis lithium chloride concentrate flow, (vi) concentration of the reverse osmosis lithium chloride concentrate by electrodialysis to obtain a lithium-containing dialysate flow and an electrodialyzed lithium chloride concentrate flow, (vii) chemical purification of the electrodialyzed lithium chloride concentrate from calcium, magnesium and sulfate ions, (viii) ion-exchange purification of the chemically purified electrodialyzed lithium chloride concentrate, (ix) boiling down the electrodialysis lithium chloride concentrate subjected to ion-exchange purification with salting out and separation of sodium chloride and potassium chloride crystals, (x) producing a pregnant lithium chloride solution by diluting the boiled-down lithium chloride concentrate with demineralized water, (xi) electrochemical conversion by membrane electrolysis of the pregnant lithium chloride solution to produce cathodic hydrogen, anodic chlorine, and an aqueous solution of lithium hydroxide as catholyte, (xii) boiling down the LiOH solution, (xiii) crystallization of LiOH·H 2 O from the boiled-down LiOH solution.