It is indeed possible for lobster to be undercooked and there are some dangers associated with that. You will need to make sure that the lobster you are cooking is heated up to 145 internally. By eating undercooked lobster you can risk ingesting potentially dangerous bacteria which can cause a whole range of symptoms, including vomiting, fever, and diarrhea. You will typically start to experience symptoms of food poisoning within 24 hours of ingesting the bacteria, though it does vary depending on the type of bacteria that is ingested as well as the amount which is eaten.
Another risk that is associated with undercooked lobster meat is parasitic infection. You will find that these parasites consist of tapeworms and roundworms which can cause a lot of damage once they work their way into the digestive tract. This is precisely why it is important to make certain that your lobster is cooked all the way through so you do not risk poisoning yourself.