first,the character should be "谎" o(∩_∩)o the conversation is grammatically correct. but if a sentence has two or more different meanings, it will be not completely right, because it may cause misunderstandings. however, as far as i see, the conversation you showed is completely correct. the word"哪里" doesn't mean "where" cuz there's a sentence after it. there's only one meaning of the sentence.

Tzu-cheng 正解 A:听说他要去美国留学? B:哪里/哪有，他说谎了吧。 根据B的话推测A是听“他”说的，所以要去美国留学的可能性大一点

A已经说是去美国了所以B的「哪里」不可能是问地方意思应该是「哪有」的意思，所以我觉得他的语句没有错。 不过这个情况说哪有会比较好，比较少误会。

A, 听说他去美国留学了？ B：去了哪里？他说谎了

这里要注意 他（要） 还是 去（了）