All right, it seems that you are troubled by some problem. Anyway, you should know that lines under eyes could be seen as a sign of aging and a lack of attention to your looks. As a matter of fact, a lack of sleep, to some extend, could make your lines under eyes worse. However, it is primarily resulted from aging, or a lack of cosmetics, such as eye cream or something. Try to take care of your eyes through a better diet and cosmetics. Also, avoiding have less sleep and try to get to sleep on time.
Yes, it is possible for you to get the lines under the eyes because of the lack of good sleep. Once you get the lack of sleep, your body will work in disorder. Your blood circulation will be affected too. You will feel dry at both the eyes and the skin. You should have the good rest for the eyes. And you should use some eye drops and some oil essentials to adopt on the eyes skin.