The . . . . . . . . sounded lame to her and she did not want to give in.

The correct answer is A. excuses.

Explanation:

The word “lame” means “unconvincing or ineffective”. In this case, the speaker is saying that the excuses that the other person is making sound unconvincing and she does not want to believe them.

The other options are not as likely to be described as “lame”. Statements are simply things that are said, and they do not necessarily have to be convincing. Promises are also things that are said, but they are usually intended to be kept. Observations are things that are noticed, and they do not necessarily have to be convincing.

In conclusion, the correct answer is A. excuses.