Don't worry. It won't hurt you if there are no wounds or ulcer in your eyes before. Just wash it away with running water.
When you have washed your eyes, see if you feel uncomfortable. Do you have symptoms like redness, sensitivity to light, or watering? If so, you may need to go to see a doctor.
Ok, it looks like there is some trouble with your eyes. Let me see. Here, it is true lemon juice might be irritative to your eyes, since it is highly acid and strong, which may leave your eyes painful. Anyway, you should try to flush your eyes with some water, then get some eye drops to help with them. Of course it is harmful, and dangerous. Try no be careful with it.
It is bad for you to get the bit of lemon juice in your eyes which will stimulate your eyes. You could wash the eyes with clean water and get it out. After that you could use the clean cloth to dry the eyes. In addition, you could also find the clean cloth and hot water to do the home remedy of warm compress to make your eyes feel comfortable.