Clayton registered a hat-trick of ton-plus finishes against English debutant Lipscombe to book his place in the last 32.
"It's a very nervy first round, and Adam is a great player," he said. "If I can finish like I did tonight on the last set, I'll be okay.
"If I can play my game, they've got a tough cookie to crack," added Clayton, discussing his progression to the second round, where he'll face Dom Taylor. "Hopefully it's going to be my year."
In other first-round clashes, Martin Lukeman lost 3-1 to Max Hopp, and 29th seed Dirk van Duijvenbode beat Andy Baetens 3-2.
Connor Scutt, meanwhile, fended off a spirited Simon Whitlock comeback. The Englishman led 2-0, but was pushed to five sets by the Australian for a memorable 3-2 win.
Scutt now goes head-to-head with Gary Anderson in an intriguing round-two encounter, while Hopp will face Luke Woodhouse, and Van Duijvenbode takes on James Hurrell.
Wright cruises as Menzies loses temper
Two-time champion Peter Wright also progressed earlier in the day with a 3-0 victory over Noa-Lynn van Leuven, despite a modest scoring average of 84.
Wright seized an early break of throw and punished Van Leuven’s erratic doubling to secure a straight-sets triumph.
In a contrasting first-round encounter, fellow Scot Cameron Menzies suffered a dramatic 3-2 defeat at the hands of debutant Charlie Manby, venting his frustration by punching a drinks table.
"I am sorry that I reacted in the manner that I did," Menzies said post-match.
"It’s not an excuse, but I have had a lot of things on my mind recently, and I suppose it all just became too much at the end.
"I don’t want it to take anything away from Charlie. He played well and deserved his win."
Elsewhere, Brendan Dolan edged past Tavis Dudeney 3-1, highlighted by a 170 checkout, while Mensur Suljovic overcame Canada's David Cameron by the same scoreline.
Read our full report on Monday's afternoon session
Results
Afternoon session
Brendan Dolan 3-1 Tavis Dudeney
Charlie Manby 3-2 Cameron Menzies
Mensur Suljovic 3-1 David Cameron
Peter Wright 3-0 Noa-Lynn van Leuven
Evening session
Max Hopp 3-1 Martin Lukeman
Dirk van Duijvenbode 3-2 Andy Baetens
Jonny Clayton 3-1 Adam Lipscombe
Connor Scutt 3-2 Simon Whitlock