Lines, 22, caused one of the surprises of the tournament 12 months ago at the York Barbican when he beat world No 2 Trump 6-2 in their second-round meeting.
It was a match which Trump – a former UK winner – would like to consign to the filing cabinet, under “bad day at the office”.
But Trump and Lines train together at the Grove Academy in Romford, and off the table are good friends.
That means Trump has endured some friendly banter over the last 12 months from his Yorkshire rival, ahead of their return to York this week.
“Judd is one of my good mates, so we still speak about that,” said Lines. “I remind him how he did last year at York against me.
“You just have to remind him every now and again so he doesn’t get too big for his boots,” he joked.
“I do quite a lot of practice with Judd down at the Grove, although I have been in Leeds quite a lot recently.”
Based at the city’s Northern Snooker Centre, Lines impressed in York last year, where he also beat Martin O’Donnell and Jimmy Robertson, before losing out to Marco Fu in the last 16.
“I am looking forward to York, I had a good run there last year – got to the last 16 – so have good memories,” he recalled.
“It’s close to home, too, so I am really looking forward to it.
“I always know I am capable of winning, it’s just doing it.
“I practice hard, my game is not far away, so hopefully next week it will all click into place and I go one or two further rounds than last year.”
Lines has had a good start to the season, but has been frustrated not to build on several impressive starts in tournaments.
He was edged out 4-3 by Stephen Maguire in the last 32 of the Riga Masters, then lost 6-4 to Robert Milkins at the same stage in the International Championship in China.
The latter event saw him earn another prized scalp, beating world No 3 Ding Junhui in an earlier round.
Lines has been working on mental training, to help improve his concentration levels during a hectic snooker calendar.
“This season, I just can’t seem to win that one extra match which will push me that tiny bit further,” said world No 61 Lines.
“I just seem to lose a close game, or not take my game from the previous round into the next round.
“Sometimes I do struggle with concentration. Once it goes, I find it goes for quite a while. I am working on that and my focus, so hopefully it will come together sooner rather than later.
“I do quite a bit of mental training, because it is a massive part of the game. If I can sort my mental attitude out, I know my game is in a good place.
“I think it can only make me a better player.”
Ever since Lines turned professional in 2014 – joining father Peter, 47, on Tour – the prospect of a father-and-son showdown has been a tantalising one.
The pair could meet in York, after they were drawn to meet in the third round, providing they each win their first two games. Peter tackles China’s Zhou Yuelong in his first round match on Wednesday morning, followed in the evening by Oliver against another Chinese potter in Mei Xiwen.
“I haven’t looked that far ahead,” admitted Oliver. “We can have a look if we both win our first matches.
“We have never played each other before. We have come close a few times in the draw, but it’s not gone to plan.
“We talk about it sometimes, it just wouldn’t be very nice if it happened. Although I am sure a lot of people would enjoy watching it on television.
“They would have to put it on TV, there are so many people who would want to watch it, it’s unbelievable.
“We would have all the family in the front row.”
The Lines pair are part of an eight-strong Yorkshire contingent in York this week, joining Paul Davison (Pickering), Chris Keogan (Doncaster), Adam Duffy (Sheffield), Sanderson Lam (Leeds), David Grace (Leeds) and Ashley Hugill (York).