I should have expounded more, since you basically are making sauergut. A pure strain can be used, as can most of the probiotic supplements, but some of the best lacto is naturally occurring on the grain.
Lacto like warm temps ~48c, you will certainly want to hold and maintain that until you reach your maximum acid level which will be 1.8-2.2%. Holding that temp will also kill any other yeasts that you don't want. Its as simple as making some starter wort, and throwing a handful of uncrushed grain on top. Hold at 48c for 3-5 days, the grain will sink and you can just pour the gut off the grains. You could easily make 2l use 1l and put the remaining 1l in a sealed mason jar in the fridge for later. Your acid % with this method will be about 1.25%, but its easy enough to titrate and figure it out for sure.