The source of commercial lactic acid used in consumer products is almost always carbohydrate fermentation.. The carbohydrates used are almost always obtained from plant sources.
If the ingredient label on a food product or cosmetic product says "lactic acid," the lactic acid almost certainly comes from carbohydrate fermentation.
Carbohydrate fermentation is the same process used to make beer, wine, and bread.
Here is a link to a company that produces or markets lactic acid.
Note that lactose is different than lactic acid and that lactose is commonly derived from cows' milk.
However all the chemicals that end in "lactate" are generally made by reacting lactic acid with another chemical. Thus ferrous lactate would be made by reacting lactic acid with an iron-containing compound, and would not be made from lactose or have milk used in its production. Same thing for calcium lactate. The calcium would come from calcium carbonate, that is, limestone. While limestone may be a rock made from the pressurized skeletal remains of shellfish, it is generally considered a mineral both commercially, and by vegans, since the rock was formed millions of years ago, by itself, rather than by the artifice of humans.
Note that the same company I linked to above, that produces lactic acid, also produces potassium lactate, ammonium lactate, zinc lactate, etcetera.
Note that PETA's list of "animal ingredient and their alternatives," is full of mistakes, and their comments about lactic acid are mistaken.
PETA writes "Lactic Acid: Found in blood and muscle tissue. Also in sour milk, beer, sauerkraut, pickles, and other food products made by bacterial fermentation. Used in skin fresheners, as a preservative, in the formation of plasticizers, etc. Alternative: plant milk sugars, synthetics."
Yes, lactic acid is "found" in blood and muscle tissue. But this is not where commercial sources of lactic acid come from. It is not where the lactic acid that you see on an ingredient list, comes from. Rather, it comes from carbohydrate fermentation. PETA's comment, "alternative: plant milk sugars, synthetics" is just nonsensical wrong information. What they are doing is like saying "salt is found in muscle tissue, and that an alternative is sea salt or salt from salt mines." Of course salt from salt mines is not an alternative source of salt, in food, it is the typical source of salt.
Lactic acid is also "found" in sour cream. But commercial lactic acid does not come from sour cream, either, or from any dairy product. The root word of lactic acid, "lact" means milk in Latin. Perhaps, knowing this, people jump to the conclusion that commercial lactic acid comes from milk. Lactic acid was named lactic acid, because it was first discovered, in soured milk. Indeed, it is produced by bacteria acting on the milk sugars, the lactose. Thus it is not a natural constitutent of milk. It is only naturally found in sour milk, something that occurs when certain bacteria feed on the milk.
Lactic acid is however a natural constituent of muscle tissue. Lactic acid builds up in muscle tissues, when muscles are used, especially if they are used heavily. Then when they are rested, it is metabolized. Despite PETA's claim, I don't think muscle tissue was ever a commercial source of lactic acid.
Lactic acid is also "found" in sauerkraut. It got there because sauerkraut is cabbage which contains carbohydrates which fermented when natural bacteria from the air worked on them, and lactic acid was produced during this process. No lactic acid is "added" to sauerkraut. It is not an ingredient of sauerkraut. It is a component of sauerkraut. To imply that sauerkraut is a product which contains animal ingredients, as PETA does, is absurd. Worse, the same inane claim shows up in web site after web site, as people copy the list.
While conceivably lactic acid could be made, commercially, by fermentation of milk and extraction of the lactic acid that the bacteria create, perhaps it is cheaper, and safer, to ferment vegetable-sourced carbohydrates. Carbohydrate sources such as cornstarch, potatoes, molasses, wheat, barley, and rice, are likely to be cheaper than milk. Milk is more likely to support the growth of bacteria that are human pathogens, than vegetable carbohydrates.
Peta makes a similar mistake regarding urea. See EOMEO's index to materials for articles on (1) urea and urethane, and (2) nitrogen.
Sadly, EOMEO does not get as many hits as PETA. Please help EOMEO get to more people.