Learn German: Ich leihe meinem Freund das Auto.

Because Freund is the receiver of the action, which makes it the indirect object. In German, the indirect object takes the dative case. The dative form for the masculine word mein is meinem.

Why does meinem Freund come before das Auto?

When a sentence has two noun objects, the rule in German is that the dative object (the receiver, meinem Freund) comes before the accusative object (the thing being acted upon, das Auto).

Why doesn't das Auto change its ending here?

das Auto is the direct object (the thing being lent), so it is in the accusative case. Since Auto is a neuter noun, its accusative form is exactly the same as its basic nominative form. Only masculine nouns change their articles in the accusative.

Does leihen mean "to lend" or "to borrow"?

It can mean both! When you use it with a dative person like in this sentence, it means "to lend" (to give temporarily). If you want to say "borrow", you usually add von (from) or use the reflexive pronoun mir, like Ich leihe mir das Auto (I borrow the car).