The man was detained by police and removed from the building less than an hour after the threat report, the Times said. The man does not work for the newspaper but is connected to Vxi Global Solutions, which rents office space in the building.
Officers searched the building but found no weapon and the lockdown was lifted by 9 p.m., police Lt. Lonnie Benson said.
Police said the man was 28 years old, but did not immediately release his name.
A radio call went out at 7:26 p.m. notifying police that a text message sent from inside the building said there may be someone "about to start shooting," Detective Gus Villanueva told The Associated Press. The Times building is across the street from LAPD headquarters.
The Times reported that the man said he had been depressed, didn't mind killing someone, showed a co-worker a bag of bullets and said he didn't want to go to jail.
The building at 1st and Spring streets has been headquarters of the Los Angeles Times since 1935.
Several other businesses and government agencies rent space from the Times in the building, including Vxi Global Solutions, which provides customer service and technical support by phone for other businesses. A message left for company representatives by the AP was not immediately returned.