Questions & Answers about Il a oublié son rasoir; elle lui prête le sien.
Lui is an indirect object pronoun meaning “to him” or “to her.” The verb prêter is used as prêter quelque chose à quelqu’un (“to lend something to someone”), so the person receives an indirect object pronoun: lui (singular) or leur (plural).
Le/La are direct object pronouns (“him/her/it”), which would replace the thing lent, not the person.