A couple tips for lacto fermentation.
1)Use a cabbage leaf over the peppers to keep them submerged in the brine.
2)Make sure you use canning salt or at least a salt with no iodine or anti-caking agents added.
3)You can speed up fermentation a great deal by using a starter culture like juice from homemade kraut. You can buy starter cultures such as Caldwells but they are expensive. Farm House Cultures sells a drink product called Gut Shot for about $5 a bottle. You only need a couple tablespoons of it to jump start a fermentation.
4) Dont over do the salt. Too much salt will slow down fermentation.
5) Sterilize EVERYTHING with campden tablets or powder. You can get them at any brew shop. Make sure your bottles, jars, knives and utensils are all sterile before you begin.
6) Use bottled water, it dont need to be fancy just no chlorine. Boiled tap water will also work.
Now, by speed up im not talking about being ready sooner. Im talking about establishing a "good bacteria" environment faster so they will prevent bad bacteria. Bad bacteria and yeast don't like low oxygen or acidic environments. Lacto B and the other good bacteria don't need oxygen and thrive in low pH. As they eat sugar they produce CO2, acetic acid and lactic acid. So once they are well established about the only thing you might get is some kahm yeast on the surface. Its harmless but to the novice it appears to be mold.
A good fermenter is a worthwhile investment. I use a fermenter made for kimchi. You can find them at Asian markets or on Amazon. The most common brand is E-Jen. They have an inner lid that holds down the veggies and limits oxygen contact.
https://www.amazon.com/jen-Kimchi-Conta ... B00SWBJJQ0
Another option is the Easy Fermenter with lids, pump and weights. They fit any wide mouth Mason jar.
This one does not include the weights but those are easy to find or just use the cabbage leaf.
https://www.amazon.com/Easy-Fermenter-W ... B01DJVVORE