Now, I would normally regard this as crackpottery of the worst kind. However, I tried everything else to no effect, so.... why not? Also it was free because I cook with coconut oil a lot** and a friend donated 16 drops of lavender oil.
This extremely unscientific treatment brought to you courtesy of the excellent Nicole, who posits that the oil penetrates the biofilm and kills it dead (hand wave, hand wave). Just think how hard it would be to organize a RCT of primarily-nipple-involvement mastitis/blocked ducts with lavender oil. I find that for once, I couldn't even care less about there being a plausible mechanism.
I still draw the line at homoeopathy, though. A girl has to have some standards.
* 8 drops per tsp coconut oil; I have no idea if the carrier oil matters. Probably anything semisolid would work.
** Because dairy is as poison unto me.