Drinking expired lemon juice can make you sick if the expired lemon juice contains any bacteria, toxins or other viruses after becoming sour.
If you just took a sip of the expired lemon juice then you're unlikely to get sick but if you drank more than a sip or a cup of expired lemon juice then you could likely get sick and get food poisoning from it.
If you have any expired lemon juice the best thing you can and should do is just throw it out to avoid getting sick.