Cowboys owner Jerry Jones has said he wants to work out a long-term deal for Austin, who broke out last season with career highs in receptions (81), yards (1,320) and touchdowns (11). Austin also received his first Pro Bowl selection.
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.
Lutui has been the Cardinals' starting right guard since 2007, but he might face competition for his job this offseason. Reggie Wells is the Cardinals' left guard, but either he or free-agent signee Alan Faneca could switch to the right side.
Faneca, a nine-time Pro Bowl selection, played left guard for the New York Jets, who released him this offseason after two seasons. Faneca spent 10 seasons with the Pittsburgh Steelers before joining the Jets.
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.