Lee, who was the Cardinals' second-round draft pick in 1986, signed a contract worth $900,000, reportedly the fourth-highest for a kicker in National Football League history, but never performed as well in the pros as he did at UCLA.
Lee made 8 of 13 field goals last season before undergoing arthroscopic surgery on his knee and missing the last five games.
"We need to kick off deeper," Cardinal Coach Gene Stallings said. "We need to make more field goals, too, which we have not been doing. Last year I blamed it on the snappers and protection, but not this year. Somewhere along the line, you have to produce."
Gallery made a 43-yard field goal in his only attempt in an exhibition game this year. Six of his 14 kickoffs were touchbacks, a Cardinal spokesperson said.