According to a quick check on Google, Hartmann's contains other salts besides sodium lactate, including calcium chloride. Calcium ions react with sodium soap to form insoluble soap -- soap scum in other words. It doesn't make sense to me to intentionally make calcium-based soap.
I haven't done the math to see if the concentration of sodium lactate in Hartmann's is even high enough to be useful in soap. A very rough estimate suggests it's probably borderline or too low. You'd want to do the math to confirm this if you plan to try this.
The other issue is cost. Hartmann's costs about $10 US per liter and you will need to use a fair bit of it in soap to get a decent dose of sodium lactate -- up to the full amount of water-based liquid you need to make a batch. That makes Hartmann's a very expensive ingredient for soap making, assuming the calcium content isn't an issue for you.
Sodium lactate as a 60% solution is about $15 US per liter, but only a few tens of grams are needed per batch.