Arguably the greatest pitcher of all time finally got his shot to pitch in the World Series in 1924. He got his jitters out by losing two games but winning Game 7 out of the Bullpen.
In 1925, the Big Train was rolling for the repeat, winning Games 1 and 4. When the Pirates forced Game 7, it was no problem. Johnson was rested and ready.
Washington gave him a 4 run cushion before he even took the mound and the World Series was a foregone conclusion. But the Pirates kept battling and in the 8th inning, Kiki Kuyler doubled home the go ahead run. The 9-7 win was saved by Red Oldham, a personal obsession of mine.
Koufax was one of the most dominating forces in baseball history in the mid 1960s and rose to the occasion in the World Series, winning the MVP in the 1963 and 1965 Series. When the Orioles roughed up Don Drysdale in Game 1 of the Series, there was no panic in Los Angeles. Koufax was going to take the hill.
For the first 4 innings, it was vintage Koufax. But the Dodger defense betrayed him, committing 6 errors over all. Koufax lasted only 6 innings in the 6-0 loss, which turned out to be his final game. Future Hall of Famer Jim Palmer got the win.
Bob Gibson had already won 2 World Series MVPs but the 1968 series was looking like his masterpiece. He struck out 17 in the opening shutout and threw another complete game win in game 4 (his 7th straight complete game World Series win.)
In Game 7, he was throwing a 1 hit shutout into the 7th when Curt Flood slipped and couldn't catch Jim Northrup's 2 out fly ball which turned into an RBI triple. The Cardinals wouldn't recover and the Tigers won the game 4-1 to clinch the series.
The A's and Dave Stewart learned their lesson after losing the 1988 World Series to the Dodgers. They were 12-1 in the 1989 ALCS and World Series and 1990 ALCS combined. And Dave Stewart was the MVP of the '89 World Series and '90 ALCS. He was unquestionably the best big game pitcher in baseball.
He took the mound against the Reds ready to dispatch of them quickly to give Oakland back to back titles. Eric Davis had other ideas, homering off of Stewart in the first inning.
Stewart lasted only 4 innings and the Reds won 7-0. Stewart would regain his stuff for Game 4 but still lost, 2-1 as it was the Reds who pulled off the sweep.
So there you have 5 examples of guys who had bigger reputations than Cliff Lee who couldn't get the job done.
I'd think of more but that should give you a strong foundation. If Koufax and Gibson can lose the big game, why not Lee?