It is very common that the expression, 'sucking a lemon' is used to show a sad or negative feeling. When a person is sad and it reflects on his or her face, they are usually called in a way that they sucked a lemon.
It could be said that lemon is used because of its sour taste, so I'm the sourness then reflects on the face of the person sucking it.
It's why the old saying goes, when given a lemon you should make a lemonade with it. Which means you should convert the sad and negative things or feelings given to you to something worthwhile.
So, the bottom line is that having a face like when he's sucking a lemon is a sad and negative face.
Which in reality, whether you are passing through a lot or even sucking a lemon, you should try to keep a straight face. It really helps.
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