If you have an FTIR machine, IR absorption spectroscopy can give you mM concentrations of lactic acid in solution. It also allows you to distinguish lactic acid from lactate salts.
However, HPLC or GC/MS would be the most sensitive methods.
The method may depend on your instruments available. We use in our lab a very simple and inexpensive method, which may be applied to any photometer you have:
lactate + O2 rects with lactate oxidase to pyruvate and H2O2
H2O2 + 4-aminoantipyrin + TOOS are catalysed by peroxidase to a violet chromogen and 4H2O
The choice of your measuring method depend mainly on the degree of accuracy you're targeting, the «purity» of your fermented broth. The following two links will take you to Barker and Summerson as well as Barnett's methods and both are colorimetric.
If your fermented broth contains mainly lactic acid (i.e. not a blend of organic acids), you can have an approx. value by simply checking titrable acidity, which the most elementary way to estimate the overall acid content in a given matrix.