Lawes, playing his 100th Test match - 95 of which have been for England and five of which have been for the British & Irish Lions - led from the front in Brisbane.
He delivered a gargantuan 80-minute showing that helped England to overcome a Wallabies side who had won the first Test 30-28 a week earlier.
And former Saints and England captain Hartley feels Lawes taking on the role of skipper has been a big help to Saracens back Owen Farrell.
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"It means Owen can purely focus on himself because Eddie (Jones) has been quite vocal in saying he wants him to focus on his performance after coming back from injury," said Hartley, working as a pundit for Sky Sports.
"Being in that role, there's a lot more to it than just playing - it almost distracts you and pulls you away from your own performance.
"Courtney being captain frees Owen up to be the ultra-competitor that he is - and he was very assured, very pragmatic and he just did the basics very well.
"And Courtney's cool, man - he's so calm in that role and he's very calm when he speaks.
"He's got good rapport with the refs, he's a world class player and the strength of that group is not just Courtney.
"He has the honour of leading the team out and gets to badger the ref all game, but if you look at that team sheet, there's leadership and captaincy potential in seven or eight positions.
"It frees Owen up to be himself and not be the diplomat he maybe doesn't want to be.
"But Courtney is very good in the role."