here's what i learned:
i used to under the impression that vegetable and fruit ferments needed to "breathe" b/c that the expression my parents and grandparents used when i was growing up. however, that is not really the case. they need to off-gas
some more violently so, and if the lid were to be on tight, you might get an explosion (ask me how i know). The process should be anaerobic, and sometimes it's achieved by submerging the stuff in the brine, but sometimes you can't do that, like with chutneys and sauces.
it's different with other ferments. my gf sourdough needs to breathe, as does kombucha.