we did our first kettle sour Gose this year. Turned out great (for the kids who like that crap, not me. Yuck). We cooled the kettle down to 80 and pitched a Lacto culture from Wyeast. Let it sit 3 days until the pH hit 3.2. Was amazed at how fast the pH dropped.
Granted, this was on a 15 bbl batch so not sure how much faster or slower a 10 gallon batch would be. It would certainly be depending on how healthy your culture is and how warm you keep the lacto.
I should send ya some yogurt to try....
I have this aversion to adding milk to my beer.