Salt-added fermentation starts out by creating an alkaline environment that discourages harmful bacteria but allows healthy, probiotic bacteria to thrive and get to work fermenting the food. Those good-guy bacteria then create an environment that continues to keep out the bad guys.
To lacto-ferment food without that first salty step you need to introduce living, good-for-you bacteria. There are two ways to do that:
Add 1 tablespoon of whey to each pint of food you want to ferment. Add enough water to cover the food. Think you don't have whey? Think again: if you have yogurt, you can have whey. Just strain yogurt through a cloth filter or several layers of cheesecloth. The thickened yogurt is yummy. The liquid that separated from it is the whey.
Add 1 tablespoon of brine from a previous ferment to each new pint of food you want to ferment. Assuming the previous ferment was never heat-processed, it should include living good-guy bacteria. For example, you just gobbled up the last of a jar of lacto-fermented green beans. There is still lots of brine in the jar. Use that to jump start your next batch.
Once you've added the whey or active brine, proceed with any lacto fermentation recipe just as if you had started by adding salt.