In a corresponding move, the Cubs selected the contracts of right-hander Felix Peña and left-hander Rob Zastryzny.
"If we have guys that need time to get rest, you give them time to get well," manager Joe Maddon said. "You don't want to push that, because on the back side, you can have a big negative. With both John and Hector, we've thought about it. Where we're at, record-wise, makes it easier, but it's still the right thing to do, regardless."
Lackey leads the Cubs in innings this season, with 158 1/3. To fill his spot in the rotation, the Cubs will turn to reliever Mike Montgomery, whose first start will come on Saturday.
Rondon has a 2.47 ERA and had been the team's closer before Chicago acquired Aroldis Chapman; since then he's pitched in the eighth inning. This is his first stint on the DL this season.
"I've always been a little tight in the tricep, but this is the first time for me," Rondon said. "I have to take it a little easy. ... It's no big deal, because I've been pitching like that for a couple games, and I haven't felt that much pain. I know I have something there that I had to take care of."
Carrying as many pitchers as possible is especially important at Coors Field, where teams have scored 12.6 runs per game, which is tops in baseball.
"It's a different place to hit," Maddon said. "The ball does carry farther. It's definitely a psychological disadvantage for pitchers. It's definitely a psychological advantage to most hitters. If someone wants to tell you otherwise, it's not true. It is true. You're playing at a mile high, and the ball carries better, and I don't think it breaks nearly as well. All the advantages point to the hitter."
The Cubs' No. 20 prospect, according to MLBPipeline.com, Zastryzny was the club's second-round pick in 2013 out of the University of Missouri. He's experiencing his most productive full Minor League season this year as a 24-year-old, posting a 4.31 ERA over 24 games (23 starts) at Double-A Tennessee and Triple-A Iowa.
The 26-year-old Pena is the Cubs' No. 25 prospect, per MLBPipeLine.com. He posted a 3.41 ERA in 36 relief appearances for Iowa this season, striking out 81 batters in 63 1/3 innings.