It left Great Victoria Street station at 4.25am and arrived in good time for fans to see Darren Clarke teeing off.
Luke said he was rooting for Phil Mickelson to win The Open but added that he was also a fan Northern Ireland golfing stars Rory McIlroy, Graeme McDowell and Clarke.
He had also done his homework on the Portrush connections with golf and said he believed the presence of the town's Ricky Elliott on the bag for Brooks Koepka could be a massive boost for him.
Mary said she was a big Rory fan, adding: "I met him once at a championship in the States and he was lovely."
The Jacksons, however, have little time for their fellow countryman Tiger Woods.
Luke said: "The girls have issues with him because of his off-the-course behaviour, but he is a great golfer."
Their train was dubbed the American Express because so many visitors from the States were on board.
Dan Blendell from Albany, New York, was on a flying visit to The Open. He said: "I've always wanted to get a taste of an Open in Britain. I'm a huge golf fan but I've never really seen a links course in the States to compare with British and Irish ones like Portrush. I've seen pictures and it looks spectacular."
Dan's partner Carol Hackett is taking him on the trip as a Christmas present but she didn't get herself a ticket for the golf.
"I'll probably go shopping," she said, but plans to accompany Dan on the next phase of their cross-Atlantic trip.
"We're going to St Andrews in Scotland because it's the home of golf.
"We're so close, we have to visit it."
Robert and Lisa Gowdy from Detroit, who were also on the train, initially planned their trip to Ireland purely for the golf but expanded the size of their party.
Robert said: "It was the lure of the golf which brought us here in the first place. We've seen all the famous championships in the States and wanted to try one over here.
"But I later decided to bring my parents, Roy and Betty Gowdy with us because they are originally from Belfast."