Well, maybe yes, lack of sleep can cause eye strain. In my opinion, if do not get enough sleep, your eyes also do not get enough time to rest. And then, in this way, your eyes can get dry more easily. And sometimes, when we are lack of sleep, the whole body suffers more dehydration in general, so this is also link to make your eyes to be dry. When your eyes be dry, it is likely to increase the eye strains on your eyes, when they are working. So it can lead to eye strain in a long term. To solve the problem, the first thing you should do is to have a good rest and make your eyes have good rest. And also, you can take some eye drops to your eyes too.