Kansas City contributed to the southpaw's cause for the third time this season as Lee pitched the Indians to a 10-3 win on Thursday at Progressive Field.
As 21,391 fans enjoyed a cloudless afternoon, Lee improved his record to 18-2 and kept his league-leading ERA at 2.43.
Grady Sizemore drove in seven runs as Cleveland completed a three-game sweep. He got the final three RBIs on a home run off reliever Josh Newman in the eighth.
The Royals finished their trip with a 1-8 record. They've lost five straight and 12 of their past 14. They're in last place, 17 games under .500.
"It wasn't a good day, it wasn't a good road trip -- going home with [a] 1-and-8 [record] is no good," manager Trey Hillman said.
He had no magical solution.
"We've got to keep working. On things that we should do better and we don't do better, we've got to keep working regardless of what the standings are, regardless of what the record is," Hillman said.
One item that's surely on his to-do list is the matter of pop flies that keep eluding his fielders. The latest example came in the second inning when shortstop Tony Pena Jr. dropped Ryan Garko's infield popup.
"Today was a sun ball," Hillman said. "Tony's got prescription glasses, flip shades don't fit over them and he doesn't have any prescription sunglasses."
The ball fell off Pena's glove for an error.
"I saw it good -- just coming down, it got in the sun," Pena said.
Royals starter Zack Greinke got a second out, but singles by Jamey Carroll and Asdrubal Cabrera loaded the bases. Up came Sizemore and Greinke felt supremely confident.
"I feel like he's probably the best hitter in baseball that I feel like I'm going to get out every single time," Greinke said. "But I don't. He finds a way."
Sure enough, Sizemore hit a high fly that dropped into deep left-center field, eluding the pursuit of Esteban German and David DeJesus, for a three-run triple.
Sizemore is a modest 8-for-28 (.286) against Greinke, but has solved him for 11 RBIs.
"I get him when I don't need to and he gets me when it's important," Greinke said.
The Pena error prolonged the inning and hurt.
"Yeah, but I usually do a good job of getting out of those problems," Greinke said. "Just the last two or three starts, I haven't been getting out of jams. I've always been good at that."
Greinke took the blame.
"All three of those hits were pitches right down the middle," he said. "Getting behind and then right down the middle -- just not executing at important times."
There was another error in the third inning; first baseman Billy Butler made an errant throw. That preceded a two-run homer by Shin-Soo Choo.
Meanwhile, Lee was cruising along with a no-hitter for four innings. Finally in the fifth, after an error, John Buck lined a single to left. Mark Teahen followed with a two-run double and scored on Pena's single.
The Royals had dinged Lee for three runs, but still trailed, 5-3.
"If we're going to get three runs off him, we should be able to win the game," Greinke said. "That was what I asked for, got it and still didn't pitch good enough to do it."
He was out after five innings, but the Indians kept adding on. Jhonny Peralta led off the seventh with a home run against Royals reliever Joel Peralta (no relation).
"That's the first one he's ever hit off me," Joel Peralta said. "I think I'd got him about 12 times."
Pretty close. Jhonny P. was 0-for-9 against Joel P. before that homer.
Sizemore, who picked up an RBI single against Robinson Tejeda in the sixth inning, belted his three-run shot in the eighth after Newman had walked two batters.
The Royals were no match for Sizemore's seven RBIs. Along the way, their chances fizzled as they hit into five -- count 'em -- five double plays.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.