Austin has until June 15 to sign the tender, which is worth $3.168 million. If Austin doesn't sign, the Cowboys could cut the salary to $1.65 million.
Lutui, a four-year NFL veteran, also has until June 15 to sign the tender or the Cardinals can lower the $1.76 million salary to approximately $600,000.
Austin and Lutui weren't alone in receiving a second tender offer Tuesday. The Minnesota Vikings did the same to defensive end Ray Edwards, according to the Star Tribune, and the Green Bay Press-Gazette reported that the Packers reissued tenders to three players -- safety Atari Bigby, cornerback Tramon Williams and defensive end Johnny Jolly.
The Associated Press contributed to this report.