Well, yes, lack of sleep can lead to red eyes. As we know that when you do not have a good sleep, it will just make your eyes tired, and stressed. In that way, it will just make high eye pressure. In the end, your eyes will be red, bloodshot. Of course, it is also possible to be the pink eyes. As we know that pink eye is a bacterial infection. And when you get it, your eyes can feel itchy, and will be red. Sometimes, it can be watery. So you should take some measures as soon as possible. You can put some ice on your eyes and change it frequently. Also, having a good rest is also important.
Yes, you could get the red eyes because of the lack of the sleep. When you go to bed too late every night, you could find that your eyes may easily get the bloodshot. You'd better have the good sleep and use some eye drops to release your symptom on the eyes. You could drink some milk before you go to sleep which could make your sleep sweet.
So, it is true that sleep deprivation would give rise to red eyes, and so does an eye strain. Because without proper sleep, our eyes grow to be stressful and bloodshot, stressful, and painful, it is a sign of sleep deprivation I suppose. So, you have to properly allocate enough time to rest your eyes from time to time and take multiple vitamins and vegetables at the same time.