She promised her father she'd be back by lunch.

Literal

She [topic-は] lunch [by-までには] return-come [quotative-と] father [to-に] promised.

~と約束した ('promised that') uses the quotative と to embed the promise content. 父親に marks the person she made the promise to. 昼食までには uses までに + は for 'by lunch (at the latest).' A clean example of indirect speech with a promise verb.