Lyle and Goggin, who shot 68 Friday, are at 9-under 135.
Paul Sheehan, a co-leader after the first round, was one shot back in third after a 70 Friday.
Six players, including last weeks Australian Masters winner Rod Pampling (67), were tied for fourth at 7 under. Australian Nathan Green, who had a hole-in-one on the par-3 11th, shot 68 and was in a group three strokes back.
John Daly, who was making his first appearance here since throwing his ball and putter into a pond off the 18th green in 2002, bogeyed his first three holes Friday and missed the cut after shooting a 77 for a 4-over 148.
Six groups completed their second rounds Saturday morning, and the cut was made at even-par 144. Defending champion Peter Lonard, at 1 over after a 75 Friday, also did not qualify for the weekend.
Six years ago, Daly was disqualified for failing to sign for a 78 on his scorecard, but would have missed the cut anyway. Daly also missed the cut last week at the Australian Masters at Melbourne. He is scheduled to play next weeks Australian Open at Royal Sydney.
On Friday, he was subdued after taking a seven on 18 ' putting two balls in the water when he knew he needed at least a birdie to make the cut. He was plagued by putting problems all week.
Daly only decided a few weeks ago to play here, but the move by organizers to secure him paid dividends ' attendance for the first two days was up nearly 5,000 from last year, despite threatening weather Friday and a late afternoon suspension due to a thunderstorm on Thursday.
The 27-year-old Lyle had nine birdies in his second round, but also had two in six holes to complete his first round early Friday morning, giving him 11 birdies in 24 holes on the day.
Lyle, who spent nearly a year in a hospital in 1999 with leukemia, was one of 78 golfers who had to complete their first rounds Friday due to an early finish Thursday because of storms that hit the Hyatt Regency resort course.
He joins five others, including Goggin, who have shot 63 on the course. The others are Australians Stuart Appleby, Wade Ormsby, and Nick OHern and American Bob Estes.
Lyle lost his PGA Tour card in 2007 after qualifying via the Nationwide Tour the year before. This year, he returned to the Nationwide Tour and finished fourth on the money list after two wins, again elevating him to the big tour.
I think what happened to me last year was possibly the best thing that could have happened to me, Lyle said of losing his card. Getting out there, playing bad, seeing what I have to do to succeed at that level and then coming back.
Not that its been all perfect ' he had a heated discussion with his father, John, over dinner on Thursday night.
I pretty much had an argument with him about everything Im doing and something kind of snapped in me, Lyle said. He wants me to play a little bit more aggressive and I think maybe I have dropped off in my aggression.
He took his fathers advice.
I think today I was perfect, Lyle said. I went at the flags when it was on and when there were shots that werent on I just tried to give myself a putt. And I holed a couple of those myself.