Lampkin, 25, has never played a regular-season NFL game.
He entered the league in 2017 as an undrafted free agent, signing with the Chiefs. But he tore an anterior cruciate ligament in training camp.
Lampkin was injured again during last summer’s training camp, and the Chiefs reached an injury settlement with him.
He joined the Browns’ practice squad Dec. 13 and signed a futures contract with the team Jan. 5.
Woodson-Luster, 23, has played 18 games the past two seasons. He has spent time with the Raiders, Bills and Browns.
Woodson-Luster played 14 games for Oakland in 2017, making seven tackles. He appeared in four games for the Browns last season, making one tackle.