Well, hmmm, I beg to differ with NDA. Lactic acid, not sodium lactate, is created by fermenting sugars or starches.
Sodium lactate is the simple salt created by reacting lactic acid with a base that contains sodium (NaOH will do nicely). This is an acid-base reaction, not a fermentation reaction.
You can ferment cane or beet sugar, cornstarch, potatoes, molasses, etc. to get lactic acid, by the way. The sugar or starch doesn't have to come from milk, although it can (yogurt, cream cheese, or truly soured milk all contain lactic acid).
If you react lactic acid with a base that contributes potassium (KOH, for example) you will end up with potassium lactate instead. So I wonder what soured milk or yogurt would contribute to a KOH (soft or liquid) soap that a non-fermented milk would not.