The move will give Cleveland more than $3 million in movable contracts to help facilitate a future deal, possibly one for the Minnesota forward.
Felix, 23, saw limited action in Cleveland after being drafted early in the second round last year, making just seven NBA appearances.
But the 6-foot-6 shooting guard has impressed with defense during stops at Southern Idaho and Arizona State. He also averaged 14.6 points and 8.1 rebounds a game during his final year as a Sun Devil.
"He's another young wing, but he's a little different from what we've got," Jazz General Manage Dennis Lindsey says. "He sees himself as a defender first. Anybody that can defend and move the ball and make the corner three, that's a role we can envision we'll have going forward. Certainly Carrick's game defensively is where he hangs his hat."
Felix's guaranteed deal is worth about $800,000 this year. He has two non-guaranteed years on his deal after that.
According to Yahoo!, the Jazz will receive $1 million to offset the cost in addition to receiving a future second-round pick from Cleveland.
Lucas was brought on last year to help mentor point guard Trey Burke. When the rookie went down with a preseason finger injury, Lucas saw time as a starter. But the journeyman's poor play eventually saw him fall out of the team's regular rotation.
Murphy and Thomas, both power forwards, were late-season acquisitions for Utah. The two played for the Jazz's summer league team last week in Las Vegas, but had no guarantees of making the final roster.