In U.S.culture, we pay almost no attention to the meanings behind names. My name Daniel, "means" "God is my judge," but my parents didn't think about that when naming me, and nobody thinks of that when they meet me. People will name a child "after" (give him or her the same name as) a family member or friend that they admire, or a celebrity they admire. Or they will choose a name because they like the sound of it, by itself or in combination with the surname. For women, in particular, it is common to _invent_ names by putting together letters to make a nice sound.
It is very common, perhaps even the rule, for people with Chinese names simply to use their Chinese names. This is particularly true if the transliteration of the name is something that looks easy to pronounce.
I honestly feel that she should just use "Ling." It sounds very nice to me.
A few that happen to start with "Li-" are "Linda" (very popular when I was a kid but very old-fashioned now!), "Lily" (which is also the name of a flower," "Linnea" (a Swedish name that has gotten popular), "Leona" or "Liona" (means "Lioness!"),