Lui/Elle

Question

I have been taught that lui refers to both male and female but in the exercise they are conceptualized differently.

Accepted Answer

One of the difficulties of learning French (although definitely not unique to the language) is that  the same word can have multiple uses and meanings. This is not limited to ‘lui’, or even just to pronouns. 
As an indirect object pronoun, lui refers to either a male or a female, and context is necessary to know whether ‘him’ or ‘her’ is the English translation. 
When used as stress pronouns, lui only refers to a male, and elle only to a female.
Attached lesson is relevant : 
https://progress.lawlessfrench.com/revision/grammar/when-to-use-lui-and-leur-to-replace-specific-people-with-him-her-and-them-indirect-object-pronouns