When it comes to producing sour beers, Lactobacillus and Pediococcus are the ones responsible for producing lactic acid.
Lactobacillus is probably the more commonly known bacteria when it comes to sour beers. Berliner Weisse and Gose style beers use it as their primary souring microbe and can be used to creatively add sourness without contributing other flavors. Its capable of producing lactic acid quickly at temperatures between 100-120F and will go dormant below 55F approx. Lactobacillus is found living on malt and pretty much all over breweries. So how do breweries restrain it when making clean beers? Hops! Beers produced with approx 8IBU or higher will help restrain the lactobacillus. There are some strains of Lactobacillus that are more hop tolerant like L. brevis. One of the biggest concerns when souring a beer with Lactobacillus is the rapid lowing of the pH which can cause an unhealthy primary fermentation and off flavors.
Pediococcus is the other common lactic acid producing bacteria used in sour beers. Pediococcus produces sourness a bit slower then Lactobacillus does and is more hop tolerant. Its capable of producing beers with a pH lower than 3.0 where Lactobacillus is around the 3.2-3.5 range. One very big difference between Pedio and Lacto is that Pedio produces diacetyl which is commonly described as buttery or movie theater popcorn. Its best to use Pediococcus with Brettanomyces so that the Brett will convert the diacetyl into less flavorful by-products. Another difference between Lacto and Pedio is that Pediococcus requires oxygen to survive. As a result you can pitch Pediococcus in primary when the wort is aerated and not be concerned about harming the bacteria and producing off flavors. Pediococcus produces a more aggressive and sharp tartness then Lactobacillus.