But they are followed by Kiwi Steve Alker, who is lurking in outright fourth at 6-under-par, and is in with a real sniff at becoming the first New Zealander to win the Open since 2003.
Alker (44), who carded a 1-under-par 70 at Millbrook on Thursday, started well at The Hills by bagging birdies on the 13th and 14th yesterday.
In much better conditions than Thursday, he tore up the front nine with four birdies in a five holes to sit 6-under, before he slipped up with a bogey on the penultimate hole of his round.
The Hamilton professional, who is now based in the United States, said he came home to enjoy himself and was not putting too much pressure on himself to perform in the final two rounds at The Hills today and tomorrow.
‘‘I didn't play a lot of golf over Christmas so I wasn't expecting so much coming back into the new year, so that probably helped,'' he said.
‘‘It was freezing [in the morning], so it took a couple of holes to get going. But once I hit 13 or 14, it stretched through there and I started playing really nicely.
‘‘I'm just focusing on playing my game, hitting my shots and everything else will take care of itself.''
Fellow Kiwi Peter Smith (56), the oldest player in the field, is tied for 10th at 4-under-par.
He is the golf operations manager at Millbrook, and has played only a handful of rounds the past five years. But everyone will be playing catch-up behind Griffin, Lawson and Tanihara when the third round starts this morning.
Griffin, who was 1-under-par after his round at Millbrook on Thursday, fired a classy 7-under-par 65 yesterday.
He started with a bang, making his move up the leaderboard after nailing two eagles in three holes.
The Victorian had a good day with the putter, holing one putt of nearly 10m to eagle the 17th and another of 3m to do the same on the first. He also drilled an impressive putt of 16m to birdie the par-3 fourth.
‘‘There are some tough holes, but there is plenty of birdie chances,'' Griffin said when asked about The Hills.
‘‘When I can get myself into contention, I usually play well. You're always nervous in the weekend, but a good kind of nervous.''
Lawson, who was in one of the last playing groups, tied Tanihara and Griffin at the top of the leaderboard after finishing with a flurry of birdies at The Hills.
The Victorian was 1-under-par heading into the day, but boosted by birdies on the final three holes, replicated Griffin's 7-under-par round.
‘‘I finished quite well. I was just being patient ... I sort of found something out there and it was good to have a good finish,'' he said.
Tanihara, who shot a 3-under-par 69 at The Hills on Thursday, followed it up with an excellent 5-under-par 66 at Millbrook yesterday.
The 37-year-old showed why he has won 11 tournaments on the Japan Golf Tour, firing a near flawless round in at times breezy conditions.
He hit off the 10th to start the day, and opened with a couple of birdies.
His only slip-up was a bogey on the 14th, before carding four more birdies on his way to the clubhouse. Australian Steven Jones, who led after the first round, dropped five shots yesterday and is tied for 40th at 1-under-par.
Manawatu professional Joshua Munn, the leading Kiwi after the first round, dropped two shots in his second round and is tied for 24th, while pre-tournament favourite Ryan Fox, of Auckland, is 1-under-par for a share of 40th.
Kiwi Josh Geary, who was considered a good chance before the tournament, missed the cut after finishing 4-over-par (tied for 94th).
Dunedin amateur Nick Borren spent the majority of the day on the edge of the cut, but three triple bogeys and three double bogeys on Millbrook's front nine saw him finish his second round at 10-over-par, tied for 130th.
●Australia leads New Zealand 5-3 after two rounds of the celebrity challenge.
Brendon McCullum beat Allan Border and Shane Cortese beat Ivan Cleary in round two, but Ricky Ponting beat Stephen Fleming and Glenn Robbins edged Justin Marshall.