The Border-Gavaskar Trophy triumph confirmed Australia's spot in a second consecutive World Test Championship (WTC) final, with the ICC's top-ranked side winning more Test matches in the past cycle than any other team.

Elder statesman Lyon saw signs of greatness in the win in Galle, where Australian appeared in control from a first over that featured three fours off Travis Head's bat. But Lyon does not feel the current crop of Australian players can yet lay claim to being a truly great side.

"We want to become a great Australian team. We're on that journey, we're not there yet. That's our end goal," he said. "Part of that journey is making sure that when we close the window, we nail it shut. It's all about being ruthless and doing our best thing for long periods of time."

The win in Galle ensured Australia would continue to hold every bilateral trophy for which they are eligible, alongside the ODI World Cup and the WTC trophy.

But Lyon was quick to point out that Australia had drawn and not won the past two Ashes series played in England, last winning outright on the road in 2001. Australia have also not won the Border-Gavaskar Trophy in India since Ricky Ponting's side took out the four-match series 2-1 in 2004.

"There's a few things [Australia needs to achieve]," said 37-year-old Lyon. "This is only me and my thoughts as well. We've got some great players within that change-room, there's no point hiding behind that. "

Australia will have to wait until 2027 for chances at away series wins in India and England. The country's greatest ever offspinner, Lyon said he "100 percent" hoped to play on that next trip to spin-friendly India as a 39-year-old.

The trio took 17 of Australia's 20 wickets in Galle, but the team does not have a subcontinent Test tour planned between the ongoing two-match series and India in 2027.

"We're going okay, but I still feel like we've got a lot of improvement to do. That's about being ruthless," Lyon said of the offspinning trio. "We're three totally different bowlers with three totally different mindsets as well. I feel like I'm learning off Todd and Matt, and I feel like they're pushing me to try and get better as well. Hopefully I'm passing on a little bit of knowledge here and there."

Lyon is mostly free of a left hip injury he suffered in the summer, though he is still in pain if he falls on the area.

"But I didn't have to land on it today, so all good," said Lyon, who took match figures of 7 for 135 in Galle. "Apparently I ripped the deep tissue off the fascia [hip muscle], whatever that means. Apparently there was a bit of excess blood or something in there. Not ideal, but all good now."