RR,
I guess I'm a little dense.

So, does it actually show Lincoln's assassination and do we see JW Booth and the aftermath?

AND, is that where the movie ends?
No. Instead of showing Ford's Theatre, we cut to another theatre where Lincoln's son Tad is watching a children's play when somebody walks on the stage and erupts with news of the great tragedy. (Which actually did happen, I believe.) Spielberg teases the audience who may've expected seeing a re-enactment of the murder, especially after Lincoln leaves the White House for his fateful engagement at Ford's Theatre. Then we cut to (if I remember correctly) Lincoln's deathbed and then close out on his 2nd Inaugural Address ("
...malice toward none, with charity for all.")
Interestingly I remember years back when Spielberg originally was going to make this (back when Liam Neeson was going to play Lincoln), reports allegedly linked cameos from Harrison Ford as Andrew Johnson and Christian Bale as John Wilkes Booth. Neither historical character showed up in the movie that the Beard did make.
Public radio interviewed Sally Field a few days ago on the film. Though I tuned in somewhere in the middle of the interview, she did a lot of research for the role and said she gained 15 pounds to play Mary Todd Lincoln.
TIS
LINCOLN Sound designer Ben Burtt* actually went to ridiculous lengths. He got permission from the Obama White House to go inside and record the sounds made by three clocks in residence that Lincoln had, the same for a few doors that apparently (unless I'm remembering this anecdote wrong) leftovers from that era. The same goes for recording a watch that (allegedly) Lincoln had in his pocket when he was assassinated.
So when (if) you go see LINCOLN, consider the sounds of the clocks and watch and doors, probably the same sounds Lincoln heard over 150 years ago.
*=A long career, but his greatest contribution was designing the sounds for the STAR WARS movies. Darth Vader's breathing, the light saber's humming, R2-D2's beeps, all Burtt's hard work.