Yes, what your grandma told you is right. The head lice will affect your eyes irritation because the nerves in the head and eyes are interlinked. You should get rid of head lice and keep the hygiene. Once you get the eye irritation, you need to use the eye drops with anti-inflammation to release the eyes. You could do the warm compress to make your eyes feel comfortable.
Generally speaking, it is not very common that head lice will cause eye irritation. However, in some cases, if the head lice are serious, or there is the damage done by the lice by human beings' scratching, which becomes infected with the bacteria and causes impetigo, the scalp may become sore and people may have a raised temperature and feel unwell. Then it may be possible that the eyes would get irritated. Head lice are small greyish parasitic insects that live only on human scalps which can be very much contagious and they have to feed on human blood several times a day to survive with their bites, saliva and faeces often making the scalp itchy and people would feel that there is something moving on their scalp. To kill head lice, people can use certain chemicals such as pediculicides, or use physical methods to remove lice and their eggs such as repeated combing.