The Lithium Ark Holding B.V. developed the reciprocal salt system
LiCl + KOH <=> KCl + LiOH
in order to produce lithium hydroxide and recover the potassium chloride. The recovery of potassium chloride is possible because its solubility increases significantly with higher temperature, while lithium hydroxide solubilty slightly diminishes in this reciprocal system. This behavior is represented in the solubility curves which represents the saturation of both salts ( Lithium hydroxide monohydrate and potassium chloride) and in reciprocal salt diagram.
Why not sodium hydroxide (NaOH)?
Sodium chloride does not increase solubility with temperature and therefor it can not be recovered and recycled separately from the lithium hydroxide.
Important to know that lithium hydroxide in water increases it solubility with temperature, but does not in presence of potassium chloride.