It's "lei" as indirect object; "lui" becomes "gli", "tu" become "ti" and so on. "Mancare" is similar to "piacere" in the sense that the subject is the object being missed or lacked and the indirect object the one missing or lacking (it does also have a transitive meaning though); so "the personality is being lacked by her" -> she lacks personality.
Great explanation. Is it not true, however, that with 'piacere' a word meaning 'by' is often used? What I'm trying to say is, wouldn't a sentence using 'piacere' be wrtiten, 'al ragazzo piacono gli elefanti,' meaning 'the boy likes the elephants' or 'the elephants are liked by the boy'? Why is it only 'le' here instead of 'a le' or whatever the construction would be (I'm not sure)? Am I misunderstanding the function of the word?