WTP: “Single girls/women living in their parents’ house generally don’t light (with the exception of chabad where girls light one)”
It’s not only Chabad.
“There is a custom to add a candle for each child born, the basis for this is that if a woman missed lighting candles (which she would have done when hospitalized, or in the olden days, confined post-birth) there is a penalty imposed that has to light one extra from then on. Now, even when the woman does not miss lighting post-birth, she still adds one for her new baby.’
I could be wrong, but I don’t think that is the only reason for the minhag.