Lee, whose work load has increased after the retirement of Glenn McGrath and Shane Warne, said he was more than willing to take the extra burden as it was better than sitting out.
"I've always said I would love to play every single game for Australia. I hate being away. I think it's because of my background and my history as well," he said.
"I had 18 months where I carried the drinks and I got so fed up with being 12th man," The Sydney Morning Herald quoted Lee, as saying.
Before the 2005 Ashes series, Lee had been out of the Test reckoning for 18 months, including a stint of nine consecutive matches as 12th man.
Those experiences, he said, had spurred him to push his body to its limits, and serve as a counterweight to notions of workload management.
Lee's heavy workload in Australia's back-to-back Tests against the West Indies has come under the spotlight in recent days.
While Stuart MacGill struggled for location and Mitchell Johnson lacked penetration, the task has fallen to Lee, and Stuart Clark, to carry the attack on the flat pitches of Jamaica and Antigua, and occasionally bowl longer spells.
Lee has bowled more overs than any of the Australian bowlers and after the Antigua Test, the 31-year-old claimed to be more exhausted than at any other stage of his career.