Jacques manque à Paul --> Jacques lui manque. -- He misses Jacques.
Jacques manque à Marie --> Jacques lui manque. -- She misses Jacques.
As you can see, the personal pronoun used for the female and male cases is the same, namely lui. Looking only at the French, you can't tell whether it's a she or a he, who is missing Jacques.
"Elle" would not be correct in this context, because elle is not the personal pronoun for an indirect object.
Elle manque à Sean. --> Elle lui manque. -- He misses her.
In this example, "elle" is the subject and not the personal pronoun for the indirect object.
