She made an excuse for being late.

Literal

She [topic-は] lateness [possessive-の] excuse [object-を] did.

言い訳をする ('to make an excuse') is the standard expression — 言い訳 literally means 'saying + reason,' i.e., an excuse or justification. It carries a mildly negative connotation: excuses are generally seen as self-serving in Japanese culture.