Teams that lead an NHL best-of-7 playoff series 3-0 are 188-4 (.979).
"We're always confident we can get the next one," Lehner said. "Unfortunately, the last couple of games, we haven't gotten it. But coming in 2-2 into the third period, I thought I was playing well. I had a bunch of saves. It comes down to that play. I [messed] up."
Curtis McElhinney made 28 saves for Carolina, becoming the oldest goalie to start his first Stanley Cup Playoff game.
"I thought we did a great job," the 35-year-old said. "I think it was even a little tighter than the last game we played (a 2-1 win). It was a great effort and a huge third period for us again."
Devon Toews and Josh Bailey scored for the Islanders, and Lehner made 33 saves.
"It was a mistake; I own that one," Lehner said. "Tight game. I think we had chances, I think they had a lot of good chances. It came down to one play."
Carolina took a 1-0 lead at 6:41 of the first period. Teuvo Teravainen played Jaccob Slavin's shot from the left-side boards off his right skate for a tap-in at the right post.