The present invention relates to an improved process for the preparation of lactic acid and or lactate from a magnesium lactate comprising medium. In said process, magnesium lactate is reacted with a hydroxide of sodium, calcium, and/or ammonium at a pH range between 9 and 12, preferably between 9.9 and 11, to form a lactate of sodium, potassium, calcium and/or ammonia and magnesium hydroxide. With the process according to the invention a lactate salt is formed and magnesium hydroxide. It is essential that said so-called SWAP reaction is conducted within a specific pH range: It was found that when conducting the SWAP reaction at a pH range between 9 and 12 magnesium hydroxide particles are formed which can easily be separated from the lactate salt solution formed.