Methods and systems for producing lithium hydroxide and lithium carbonate are described. One or more embodiments involve reacting potassium hydroxide with lithium chloride or lithium nitrate to create a reciprocal salt system, and precipitation to form lithium hydroxide and potassium chloride crystals, potassium nitrate crystals, or any combination thereof. In certain embodiments, lithium chloride feedstock, nitrate feedstock, or mixture thereof, is obtained by reacting lithium sulfate with calcium chloride, calcium nitrate, or combination thereof. Additional embodiments include producing lithium carbonate, including, but not limited to, by reacting lithium hydroxide with carbon dioxide.