Lidge is 0-0 with two saves and a 5.14 ERA in seven games with Washington this season. The 35-year-old reliever has missed the past 38 games because of an abdominal injury.
Lidge gave up one run in 1 1/3 innings during a two-game rehabilitation assignment with Class A Potomac. He rejoined the Nationals for Thursday's game against the Mets.
Rodriguez is 1-3 with nine saves and a 5.14 ERA in 24 games. The 25-year-old has a strained right index finger. The move was made retroactive to Wednesday.