The watch is the Rolex of it's time. While we have come to believe that AL was a humble man of simple trappings, that certainly was not the case with MTL. She made sure her husband had the finest things available. His suits were beautifully tailored, his boots were custom made, he had all the best.
I think that may be the watch that was actually used in the Lincoln movie (2012)?
I remember reading that the ticking heard in the film was from Lincoln’s timepiece.