Lucas was a restricted free agent with an original-round tender, and Butker and Hamilton were exclusive rights free agents.
Lucas, a sixth-round pick of the Dolphins in 2016, played all 16 games for the Chiefs last season after a trade from the Dolphins at the end of training camp. He made 32 tackles, a sack, an interception and two pass breakups.
Butker, 23, has kicked in 29 games for the Chiefs the past two seasons. He is 62-of-69 on field goals, with a long of 54 yards, and 93-of-97 on extra points.
The Panthers made him a seventh-round pick in 2017, but he never kicked for Carolina.
Hamilton, 25, appeared in one game with the Chiefs in 2017 and four last season. He also played three games for the Eagles in 2017.