The British were the first to fire at Lexington and Concord. There are two testimonies that claim that the British are the first to fire. One of the testimonies are from a lieutenant from the British army. The other is a testimony from a Commander of the Militia. There's also the given illustration.
The first testimony from the Commander of the Militia is John Parker. He is a credible resource to believe because he was there himself. He states that his men did not open fire first but the British did. John said he ordered his men to "disperse, and not to fire". He also states that "immediately said Troops made their appearance and rushed furiously, fired upon, and killed eight of our party..".
The second testimony came from a man who he himself was with the British army. Edward Thoroton Gould, the kings lieutenant, stated that, "upon which we engaged and gave the first Fire". A man from the British army himself saying that they did fire first is far most credible since he is on the opposing said. Gould also says that it was the first engagement of Lexington.
In the given illustration, it shows the British arriving in Concord or Lexington. The Militia are running away while as it seems, the British are firing their guns. I assume this because their are bodies lying on the floor on the Militia side while gun powder is shown on the British side. The illustration shows the destruction of the town and of the many people that died.
I believe in my three reasoning because they are credible. John Parker was present at the scene when it had happened and also Edward Thoroton Gould. Especially Gould's testimony because he was on the British side. The illustration, although not really credible, it still showed what many of the testimonies had said. This was a difficult task to choose if either was really the first to shoot, but I believe that the British were the first to shoot.