The Broncos linebacker has talked openly about breaking Michael Strahan's single-season sacks record. Strahan had 22.5 in 2001.
Lawrence wants it, too, and he wants to get it before Miller does.
"My goal is to be the best that's ever played this game," Lawrence said Saturday at SportsCon 2019 in Dallas. "For sure, I want to beat that sack record, make it my own, so he can talk about beating my record. I'm going to just wait until I get to the season and then worry about sacks."
Lawrence, 27, had 14.5 sacks in 2017 and 10.5 last season and got paid for it. He signed a five-year, $105 million deal this offseason.
The two-time Pro Bowler delayed shoulder surgery until getting his money, so Lawrence didn't go under the knife until April.
Private defensive line coach Brandon Jordan recently posted video of Lawrence using his shoulder while working out in the sand.
"The mobility and my strength is coming back naturally," Lawrence said. "I'm working every day. I'm able to do things. I'm just still limited. Just taking my time. I've got time still."
Lawrence is expected to start training camp on the physically unable to perform list, although he said Saturday he has no idea what the plan is.
"My main thing is to be ready by Week One," Lawrence said.