The 21-year-old followed up his shock 6-2 victory over world No 3 Judd Trump by whitewashing Jimmy Robertson 6-0 at the York Barbican.
The former European Under 21 champion faces veretan Marco Fu on Wednesday night in front of the BBC cameras with a place in the quarter-finals the prize and Lines is starting to deliver on his undoubted talent.
He has banked £15,000 for reaching the last 16, the best run of his rookie career, but now wants to emulate Grace.
Both are from the Northern Snooker Centre in Leeds, and Grace was the fairytale story 12 months ago when against the odds he reached the semi-finals.
“I watched David Grace here last year, he is from Leeds as well, and I told my dad that would be me next year,” said Lines. “It was more in hope really.
“Now I am here, I hope I can go all the way.
“I played very well today and handled the occasion a lot better than Jimmy did.
“I made a few one-visits at crucial times. I have been practicing a lot on my scoring and I couldn’t really see it in matches until recently.
“I think I could win it, I’m playing well enough to win it.”
Lines reached the last 32 after beating Martin O’Donnell 6-5 before causing a huge shock by knocking out former world No 1 Trump.
After a season which has seen the 21-year-old suffer some tough draws, finding his route to getting deep into a tournament blocked by the likes of former world champions Neil Robertson, John Higgins and Shaun Murphy, his victory over Trump could prove to be a watershed moment for Lines.
The world No 61 is managed by Django Fung, who manages players like Ronnie O’Sullivan and Trump, and has regular training sessions at the Grove Academy in Romford, Essex.
Lines raced into a 4-0 lead, edging the first two frames before breaks of 90 and 51 saw him head into the mid-session interval in high spirits.
And he swiftly completed his whitewash, knocking in breaks of 67 and 72 to earn his place in the last 16. In contrast, world No 36 Robertson, 30, only managed to score 117 points in the entire match.
It was a clinical display from Lines, who has a strong safety game, but also scored heavily yesterday.
“I just needed the big win on the TV, for my own mind, so I could start believing I can do it on the big stage. I felt very confident, that was probably from beating Judd, and it’s just belief why I am still ranked quite far down. Hopefully, I can push on.”
Lines revealed training partner Trump had sent him a text message before Tuesday’s match.
“It was a relief to win. Judd messaged me, saying ‘You’d better not lose this game’,” Lines said.
“He said if I lost this game there’d be a fine – because we’re from the same management.
“Obviously he was joking but hopefully I can push on now because I’m feeling very confident.
“Once you get a big win, if you lose in the next round it doesn’t really mean anything.
“I have never won 6-0 before so I am hoping it is the start of something good.
“There was a little worry, I just didn’t want to beat Judd and lose in the next round. Everyone would just say it was luck. Now I have shown I can do it, not just in one match, but beat a player of Jimmy’s quality comprehensively,” added Lines, who is guaranteed to rise to at least 53rd in the world rankings next week.
It has been a memorable week for the Lines family in York. Father Peter, 46, and Oliver became the first father-and-son to reach the last 32 of a ranking event since Geoff and Neal Foulds achieved the unlikely feat in 1986.
Peter – now competing as an amateur after falling out of the world’s top 64 – caused an upset of his own, beating defending champion Neil Robertson.
Son Oliver, though, nudged his father out of the sporting headlines with his Trump win.
And whatever Wednesday’s result is against Hong Kong’s Fu, it promises to be a merry Christmas in the Lines family with Oliver splashing out on gifts for sisters Lucy and Penny, plus stepmum Sarah.
“I’ve got a few texts from my two sisters already asking what I’m getting them for Christmas,” he said. “I haven’t really thought about what I’ll do with the money but obviously it’s a nice bonus isn’t it, just before Christmas. But hopefully I’m not finished yet.
“I’ll have to treat my stepmum as well because she’s always here supporting. She’ll be getting a good treat this year.”
Victory tonight could set-up a mouthwatering clash with snooker legend Ronnie O’Sullivan, but Lines knows he faces a tough challenge first against Fu
“Marco is world class,” said Lines. “He has not done what he has done in the game for no reason.
“He scores very heavy and I know I will have to be at my best to have any chance of beating him.”
Welshman Matthew Stevens – a UK winner in 2003 – set up a fourth-round clash with O’Sullivan after a 6-2 victory against Joe Perry.
Former world champion Shaun Murphy edged out Dominic Dale 6-5, the same scoreline which saw Mark Williams account for Ricky Walden.