Allegedly is the key word. If Lamon was given an arrest warrant for Taney then why didn't he execute it?
Lamon said that the arrest warrant was Lincoln’s response to Taney’s Ex parte Merryman ruling finding the suspension of habeas corpus unconstitutional.
Lamon claimed that Lincoln told him to execute the warrant at his own discretion unless otherwise directed. Lamon never gave any explanation for why he didn’t follow through with it.
Lincoln appointed Lamon United States Marshal for the District of Columbia in 1861 and he held that position until Lincoln’s death. Lamon was constantly in Lincoln’s company and he was the US Marshal, so he was in a position to have been given such an assignment if there ever was one. But we have only Lamon’s account that there was such an arrest warrant issued.