It would seem that the leniency employed with regard to allowing regular beer without kosher certification would not necessarily apply to sour beer. See e.g. Beer for Dummies:
Likewise, if beers with higher alcohol content require fermentation with yeasts other than typical beer yeast, the beers require certification.
While traditional sour beer may have been made by just allowing the beer to brew naturally, modern brewers typically prefer more predictable processes, that may introduce halachically questionable ingredients, such as the addition of nonkosher wine. Similarly, while some authorities have been lenient with regard to whiskey aged in nonkosher sherry casks, the controversial reasoning presented was that the sherry cask did not improve the taste of the whiskey, and therefore was not halachically significant. This argument is harder to make with regard to sour beer, where the taste difference is significant and desired by those who prefer it. See, e.g., here:
Patrick Rue launched the Bruery, his Belgian-style brewery in Placentia, last year, and sours have been a focus from the start. At its first-anniversary party in May, it had a four-tap sour bar, including Cuvee Jeune, a young lambic aged in Chardonnay barrels for 10 months. White Zin is a sweeter variation on Cuvee Jeune, blended with a brew made with Zinfandel grapes. Gypsy Tart was Rue's limited-edition Flanders red that was untouched by wood, and plenty sour.
Based on the same article, at least one sour beer brand may be less problematic than others:
Very few American brewers take the time (and risk) to let natural bacteria take its course, but that's what brew master Ron Jeffries is doing at Jolly Pumpkin Artisan Ales in Dexter, Mich. America's only 100% oak-aged sour brewery uses wild yeasts that appeared in the brewery naturally and spread from barrel to barrel during transfers.
The following paragraph in the article also seems to suggest that Allagash Brewing Co. of Maine also produces a sour beer without resorting to additives.
(Notably, the Talmud [Avoda Zara 31b] also prohibits drinking beer in a pub or bar, though later authorities suggest leniencies in certain contexts.)