Depending on the context, it can mean "She has a short life" (like when you know that she would die young) and also can mean "She's not enjoying life as much as she should" (when you talk about a shy, introverted person, or one with no social life).
So in Romanian this phrase is taken literally? Essentially being the opposite of what it means in English - where to "live a little" is to spend time doing fun things, as opposed to not living at all (being boring and doing nothing). In English we'd never use this phrase literally to denote a short lifespan.
My Romania partner says it has no special meaning in Romanian. So it is probably just a translation of the English sentence which has the meaning: to spend time doing enjoyable things.