Serious Eats: Talk
Fermented pickles: Is organic really necessary?
All the recipes I've found online for lactofermented pickles specify organic.
In the dill pickle episode of Good Eats organic wasn't mentioned but Alton Brown was specifically shown picking up the cucumbers at his local Whole Foods rather than his local megalomarket.
I'm not sure if the sites are telling me to use organic because they're written by hippies for hippies or because modern processing really does leave non-organic vegetables devoid of the necessary bacteria for fermentation.