It is understood the gunman was also employed by the TSA, and opened fire on his colleagues.
The gunman is now in custody, according to police.
"It's like a ghost town": Virgin Australia passenger Alexander Reid took this photo from the VA1 Boeing 777-300ER, which is sitting on the tarmac with 361 passengers on board. Photo: Alexander Reid
At least "three or four" other TSA employees were injured in the attack.
Terminal 3 is one of nine terminals within the LAX complex.
Since 2012, it has been the terminal base of the airlines JetBlue, Spirit, Virgin America and Virgin Australia.
Virgin Australia's daily flight, number VA1, landed at the airport minutes before it was closed to air traffic at 10am, local time.
I'm currently in TBIT at Gate 119. It's an absolute disaster in LAX.
Nothing moving.
My Twitter handle is @pascaljosh
Another witness, Australian school student Josh Odermatt, was evacuated from inside the terminal after it was placed on lockdown.
Mr Odermatt said police swept the airport room by room ahead of evacuating passengers and staff.
He said police told passengers to "step around" any bullet casings or blood, in order to protect potential evidence.
"The police are doing an incredible job, and grateful that we are all safe," Odermatt later posted on Twitter.
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The 7am ABC radio news is not reporting any deaths, but some injuries. I hope the terminal can be secured soon, and flights resume. Looks like there are a few AFFers caught up in this. Stay safe.
News reports are not sure if the fatality was the gunman or victim.At least one death is being reported here.
Wow, it must be bad!!!This is definitely worse than the normal LAX confusion.