This is the famous speech in which McCarthy first alleged that he had a list of over 200 communists who were working in the State Department. McCarthy refers to Lincoln in this speech for two reasons.
First, he refers to Lincoln because the speech was being given on Lincoln Day, a few days before Lincoln's actual birthday. This gave McCarthy a good reason to start the speech with a reference to Lincoln. Mainly, though, McCarthy mentions Lincoln to try to connect himself with one of our most revered historical figures. Lincoln really has very little connection to the substance of this speech. McCarthy says that Lincoln hated war and so it is sad to be unable to say that there is peace in the world on his birthday, but this is a very tenuous connection to Lincoln. McCarthy is mentioning his name to try to give the idea that somehow Lincoln would have approved of what McCarthy was saying.