Littler underlined his status as world number one with a comfortable 6–1 victory over Lim, who turns 72 next week and became the oldest player to win a match at Ally Pally last month.
Leung, ranked fourth on the Asian tour, delivered the shock of the round by beating tenth-seeded Danny Noppert 6–3.
Elsewhere, Michael van Gerwen swept past Nitin Kumar 6–1, Stephen Bunting eased to a 6–1 win over Toru Goto, and Nathan Aspinall matched that score against Lourence Ilagan.
Gerwyn Price produced the most one-sided result of the session with a 6–0 whitewash of Alexis Toylo, before Luke Humphries closed out his match against Ryusei Azemoto at 6–2.
The day’s action concluded with Gian van Veen rounding off the schedule by seeing off Motomu Sakai 6–2 to join the rest of the quarter-finalists.
More to follow...
Results
Luke Littler 6–1 Paul Lim
Man Lok Leung 6–3 Danny Noppert
Stephen Bunting 6–1 Toru Goto
Nathan Aspinall 6–1 Lourence Ilagan
Michael van Gerwen 6–1 Nitin Kumar
Gerwyn Price 6–0 Alexis Toylo
Luke Humphries 6–2 Ryusei Azemoto
Gian van Veen 6–2 Motomu Sakai