If he did not pay, Travolta told the jury, Lightbourne indicated he would use against him a consent document that the actor initially signed refusing to have his son Jett sent to a local hospital. The document cleared Lightbourne of any liability.
"They were stories that would imply that the death of my son was intentional and I was culpable in some way," Travolta said.
Travolta was testifying in the second week of the trial of Lightbourne and Pleasant Bridgewater, a former Bahamas senator who allegedly negotiated with the actor's lawyers for the medic. Both defendants have pleaded not guilty.
Travolta testified last week that he signed the document because he initially wanted his son flown to Florida for treatment. But Jett, who had suffered a seizure at a family vacation home on Grand Bahama island, was taken instead to a local hospital, where he died on Jan. 2.
Travolta and his wife, Kelly Preston, left the Nassau courthouse immediately after his testimony in an entourage of cars with their attorneys and bodyguards.
A Bahamian attorney for Travolta, Allyson Maynard-Gibson, has testified that Bridgewater told her in a January meeting that the paramedic was talking with a woman from an unidentified American news outlet "who said it might be beneficial to him if he could show that Travolta was negligent." She said Lightbourne was also in talks with several other media companies.
The actor testified that he authorized his lawyers to contact Bahamas police after hearing about the alleged threat from Lightbourne.
The trial began Sept. 21 and is expected to last several weeks.