I looooove lacto-fermented cucumbers
I have also made them myself and experimented with fermenting carrots and garlic. I didn't find a reliable method to keep them from going bad though, especially as I cannot regulate the temperature in my apartment during summer, so it was sometimes too hot.
I also found that it's normal to find yeasts or mold floating at the top after the fermentation process, but if you remove those the stuff below is still edible. And if you then boil the liquid, let the liquid cool and then put the fermented veggies back into it the stuff will keep for some time too (though it needs to refrigerated).
It was very rewarding when it turned out right, but I often had batches go bad and it was kind of too much effort for the rate of success. I'd probably need to buy some better equipment before I try again.