Lawes led from the front at Twickenham, putting in a huge performance as he helped his country to beat Tonga 69-3.
And Boyd said: "It's a good honour for him obviously.
"Courtney is a Northampton boy and he's a world class rugby player in my opinion.
"The fact he's been thrown into that leadership role, he's more than capable of doing it in his own way, which is 'follow me'.
"I'd be more than surprised if it's the only time he leads England.
"He's determined to get through the next couple of years and he could cement himself as a truly world class player."
Lawes was joined in the matchday squad by Saints team-mates George Furbank and Alex Mitchell.
Furbank started at 10, while Mitchell made his debut from the bench, scoring one of England's 11 tries.
And Boyd added: "It's nice to see. It's great for the club.
"We have 10 guys away on international duty and we will always support that.
"It's part of our obligation to grow international rugby players, whether it's for this country or other countries.
"But it does put a bit of a strain on the squad when you get 10 of them.
"I am really pleased for Mitch and for Furbs."
Lawes, Furbank and Mitchell remain in camp ahead of next weekend's game against Australia, and they are joined in the squad by Lewis Ludlam and Tommy Freeman.
England head coach Eddie Jones has called up 34 players, who met up on Sunday at Pennyhill Park to begin preparations for the Australia game.
All players will remain with England for the entire Test week, in an agreement with clubs, PRL and the RPA. This is to help enhance the Covid resilience of the team’s boundary.
Jones said: “We’d really like to thank everyone in the game who has allowed us to keep the 34 players for the week – the clubs, the PRL and the RPA.
"We appreciate their support and it will a big help for us as we prepare for this Test match.”
England will play Australia on Saturday (5.30pm kick-off) in the second of their Autumn Nations Series matches at Twickenham.
Their final fixture is against world champions South Africa on Saturday, November 20 (3.15pm kick-off).