> Did Thomas Jefferson kill a traitor on the White House lawn as stated in the
> movie Swordfish?

This is pure fiction. There is no factual basis for the story.  According to the review 
at Steamshovel Press,  
http://www.steamshovelpress.com/altmedia8.html:

The movie Swordfish refers to "Operation Swordfish," which was a government sting
 operation, set up to ensnare drug dealers in the late 1980s. Using funds illegally 
obtained from asset seizures, this undercover operation by the Federal Bureau of 
Investigation and the Drug Enforcement Agency actually created dummy corporation 
fronts to get into the drug business. Eventually government agents and others were 
caught skimming the slush fund and stealing the money for themselves.  The premise of 
Swordfish the movie is that the slush fund created by this operation has grown to a 
whopping $9.5 billion.   Gabriel (John Travolta), a mysterious, wealthy character 
wants to hack into the slush fund and liberate the money for his own purposes. 
When Gabriel gets double-crossed by a senator involved in these murky black ops, 
he tells him, "Thomas Jefferson once shot a man on the White House lawn for treason." 

What is remarkable is how this one line in a movie could lead so many people to ask
if this event really happened.  It did not.  It is just a movie, and the idea that Jefferson
shot a man is pure imagination.