I also make kimchee. When I give the lemons (or the kimchee) to friends, I make sure to tell them that they are not, NOT sterilized preserves. In other words, eat them soon. Both seem to last for a few months in the fridge. But they aren't stuff you'd put in a jar and think it will last forever.
Right now, a friend has asked me to reserve some onion relish for my parents. This is truly good, preserved stuff. I swear, it is so damned delicious. I sent Mom some last year and she just loved it. I'm reserving a couple of jars this year. Yummy!