The 46-year-old from Leeds caused a huge upset at the Betway UK Championship when he knocked out former world champion Robertson.
It was the best win of Lines’s long career in the sport, which spans several decades, and earned him a second-round meeting with Chris Wakelin tonight.
But Lines, who now competes as an amateur after dropping out of the world’s top 64, said he considered retiring from the sport in the summer.
He was worried his presence – and losing games – could be a distraction to son Oliver, one of snooker’s rising stars.
“I don’t think anyone realises how tough it is for both of us playing, more me than him,” Lines told The Yorkshire Post. “But I think it affects Oliver as well.
“That’s one of the reasons why I thought about not playing again, after I fell off the tour last year.
“I didn’t want it to get to the stage where I was putting him off.
“The game is littered with highs and lows and nobody wants to see their dad, or their son, up and down.
“I thought maybe I should pack it in, we talked about it, but Oliver wanted me to carry on playing.
“It wasn’t because I wanted to, definitely not. I hear loads of players saying ‘I am going to jack it in now’ and I hate that. I absolutely love this game, I love it.
“But that would have been the only reason to quit, if I thought it was affecting Oliver. Seriously, I would have stopped.
“I have been working for the last 15 years, while playing, and I play because I love it.
“I never wanted to pack it in, and I wouldn’t have stopped playing entirely because I love playing snooker.”
Lines was a proud, but nervous parent, watching Oliver, 21, edge through his opening round match at the York Barbican 6-5 against Martin O’Donnell on Wednesday.
Twenty-four hours later, Lines was in the spotlight, when he beat Robertson 6-3.
“I watched Oliver play the night before and tension was unbearable as he just got over the line,” he said.
“I think that’s one of the reasons I fell off the tour, not stress, but watching him then playing, watching, playing, it’s like a never-ending cycle.
“Because he won the night before, it was such a massive relief I could go out there and enjoy my game.
“I said jokingly, afterwards, if Oliver had lost in the first round I would probably have lost easily myself. I would have been on such a downer.”
Lines reached the UK quarter-finals in 2009, but admitted he did not expect to beat Robertson, who won this tournament twice, in 2013 and last year.
“It’s a bit weird,” said Lines, who works part-time at the Northern Snooker Centre to help pay the bills. “It still hasn’t really sunk in. I wasn’t expecting to win, but I did play quite well and thought I deserved to win.
“My safety was really good, it normally is, but when I get in I have not been taking my chances. I am carving them out, just not taking them.
“It was really pleasing, in the match arena, against the defending champion and the way I played.
“How I played didn’t surprise me, it was how I held myself together which surprised me.
“I haven’t been doing that in recent times. I can play like that all the time in the club, but it’s different doing that in tournaments.
“It’s about consistency, that’s what everyone is striving for. That’s why the top players are so good.”
His performance certainly impressed Robertson, who hailed his “incredible safety play”.
“He didn’t make a whole load of big breaks but he didn’t have to because his safety was that good,” said Robertson.
“It was a tough match. He is still a great player and he showed that. He was not going to be scared. He played a brilliant match.”
Lines chalks it up as the biggest win of his career, after first turning professional in 1991. “I know I have been to the quarter-finals, beaten Mark Williams, and I have beaten people like Ronnie (O’Sullivan) and John (Higgins).
“But being out in the match arena, against the defending champion, I would class it as the best win of my career.
“Neil is a fantastic player, for me he is in the top 10 of all time. To beat him, the defending champion, was amazing.”
Tonight, Lines aims to maintain his form against Wakelin, ranked 66th in the world.