Yeah, the lemon juice containing the vitamin C which has the role of whitening may lighten the dark circles around your eyes. In addition, it can increase the blood circulation around your eyes which will directly smooth the skin around the eyes. Thus, if you work too late and have the dark circles under eyes, you may take more lemon juice.
Well, as a matter of fact, it is true that some fruits, including lemon juice, will serve to whiten your skin tone, at least to some small extent. Because lemon juice contains vitamin K and A, which is able to whiten the skin and eliminate excessive darkness resulted from some other reasons. And surely, it helps to relieve the dark circles under your eyes. And I heard that this way is pretty effective. Perhaps you should give it a try and see if it helps or not.