I would have a federal officer guarding the entrance to the box. He does not let Booth in. Booth dies in a shot out with that officer.
With Officer John Frederick Parker, becomes famous as the man who stopped the assassination of President Lincoln.
The way Lincoln was evolving on the issue of votes for Blacks. I could see the 14th Amendment barring discrimination in voting based on skin color or previous condition of servitude.
So in the south there are more black voters, this means that Democrats will find a decline in votes in their southern department. So the United States presidential election of 1876, may not be as close as it was in OTL.
You might also find more off an militant Ku Klux Klan, with them having to not only deal with black voters but also the army and police, who are brought in similar to "little rock"
Lincoln has a good working relationship with Congress. He remains in charge of Reconstruction. There is no Tenure of Office Act and of course no impeachment.
This is one of those short lived PODs. In 1868, Grant is elected. He brings his commitment to civil rights and his corrupt cronies with him. So starting on March 4, 1869, OTL returns.
No POD is ever short lived, this POD will still change things later on, since what does Lincoln do out of office?
Does he travel Europe and the Middle East? If so this will have him interact with people who would in OTL never meet him.
Will a foreign politician wish to be like Lincoln and tries to rise higher to power? Or does a child or member of the public, on seeing him wish to enter politics when in OTL, it was never an idea.
Is Grant nominated as easily as he was IOTL, does Lincoln push for a second term of National Unity Party and if so, which Democrat does Grant choose as his nomination?
Does Lincoln, suggest his Vice President Johnson, to do more with his career?
The POD for preventing the assassination of Lincoln and for that matter Garfiled, McKinley and Kennedy is better security.
How can better security help against crazed individuals who have it in their head, that they must kill the president.
Guiteau had stalked Garfield for weeks, armed with a .44 caliber Webley Bulldog revolver, no matter how much better the security is, you will always have opportunities for these events to happen.
President William McKinley died on September 14 from gangrene caused by the bullet wounds, so McKinley could have became infected after any other minor accident where his skin is open.
Also McKinley was shaking hands with the public when he was shot by Leon Czolgosz, so unless you have a security that scrutinises all of the public, you cant be safe from anything
Kennedy had security, what he did not have, was the ego that would happy sit in a roofed car.