The present invention provides a method for producing lactic acid in a recombinant yeast cell culture using glucose as carbon source comprising a first, seed fermentation stage to produce biomass wherein the yeast is cultivated in a culture medium at a pH of 5 to 7, followed by a second, a production fermentation stage with biomass from the seed fermentation to produce lactic acid, wherein the yeast is cultivated in a culture medium at low p H using a yeast strain that is engineered to have lactate dehydrogenase (LDH) activity and optionally has decreased or knocked-out pyruvate decarboxylase (PDC) activity.