The American actress, Laura Keene, was the first to recognize the escaping assassin as John Wilkes Booth, the brother of Edwin Booth, whom she had toured Australia. The play, "Our American Cousin" was very popular in U.S. and had first been seen in 1858 in Laura Keene's own theater in New York.
From "The Language of the Civil War" by John D. Wright p. 219.
President Lincoln viewed Booth in the role of Raphael in "The Marble Heart" on November 9, 1863. When they , the Lincolns, saw "The Marble Heart". they were accompanied by several people. Mary A. Clay, daughter of Cassius Clay, was one and she wrote: "In the theater President and Mrs. Lincoln, Miss Sally Clay and I, Mr. Nicolay and Mr. Hay, occupied the same box which the year after saw Mr. Lincoln slain by Booth. I do not recall the play, but Wilkes Booth played the part of villain. The box was right on the stage, with a railing around it. Mr. Lincoln sat next to the rail, I next to Mrs. Lincoln, Miss Sallie Clay and the other gentlemen farther around. Twice Booth in uttering disagreeable threats in the play came very near and put his finger close to Mr. Lincoln's face, when he came a third time I was impressed by it, and said, "Mr. Lincoln, he looks as if he meant that for you". "Well, he said, he does look pretty sharp at me doesn't he?" Source p. 243 of "Mary, Wife of Lincoln" by her niece Katherine Helm (New York, Harper and Brothers, 1928).
Booth waited for this line as he knew it would get the biggest laugh of the play and would help mask the sound of the gun shot: "Well, I guess I know enough to turn you inside out, old gal—you sockdologizing old man-trap.”