Legally, she can enter the US with her US passport (since it will not yet have expired), but she will need to renew it before leaving:
Except as otherwise provided by the President and subject to such limitations and exceptions as the President may authorize and prescribe, it shall be unlawful for any citizen of the United States to depart from or enter, or attempt to depart from or enter, the United States unless he bears a valid United States passport. (8 USC 1185 (b))
This would apply even though she is also a citizen of another country and has that country's passport.
That said, my understanding is that this law is not enforced, there are no prescribed penalties for violating it, and there are no exit checks on leaving the US. So practically speaking, if she were to not renew her US passport and depart with her German one instead, I wouldn't anticipate any legal problems arising. But it is technically against the law to do so.
(It's conceivable that the airline might raise some sort of objection. I'm afraid I don't have any specific knowledge on that point.)