A quick look at your method shows a lot of steps, and since I don't know your technical level, I can't guess where the problems might be. You'll have to satisfy for yourself that you're following all procedures.
Do you see visual changes in your sample over time? Turbidity or cloudyness can show up in any sample, and of course, scatter all light, including your chosen wavelength.
Are you satisfied that your optical instrument is warmed up, and in good working condition? Do you have a test sample, usually a neutral density filter (a piece of colored glass or plastic) and does it give stable results? Can you find a standard that will be specific for 340 nm, to be sure your instrument is up to snuff?
Do you have a lactic acid standard? That is pure L-lactic acid, to react with this kit to see if your system behaves properly with an executed kit, with no possibility of other feed components interfering.
What about the possibility that the feed contains so much, or so little, L-lactic acid that the reaction is saturating, or failing to react. You may have to try a number of sample sizes, to learn how this kit works with some feeds.