Well in this case the learned book has some explaining to do because there is one very obvious source for lactic acid and that is the lactose present in cabbage and the obvious lactose-intolerance symptoms of people who cannot easily eat cabbage.
Not to worry, it's all just words.
The first sauerkraut feremnter ferments the lactose present and then the lactic acid produced helps preserve the vegetable as it lowers pH more and a secondary, very acid-tolerant lacto-fermenter transforms the other sugars and whatever else.
