NEW YORK -- Each side of the years-long debate regarding Seth Lugo's role was on display during a seven-inning doubleheader Sunday at Yankee Stadium. Despite not yet being fully stretched out as a starter, Lugo proved in a 5-2 Game 2 loss to the Yankees that he may already be the Mets' second-best rotation option. But the Mets also demonstrated how much they struggle to compete without him in the back of their bullpen.

Striking out seven over 3 2/3 innings of one-run ball, Lugo put the Mets in position to tie the game on Dominic Smith's RBI single in the sixth. But Drew Smith entered in the eighth with an automatic runner on second, then loaded the bases before serving up a Gary Sánchez grand slam -- the first pinch-hit, extra-innings slam in Yankees history.

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The Mets had lost Game 1 of the doubleheader in similar fashion, 8-7, after Edwin Díaz allowed a game-tying homer to Aaron Hicks to force extra innings. After sweeping a doubleheader Friday at Yankee Stadium, the Mets dropped the final three games of the five-game series.

"It doesn't matter who it is, whether it's the bullpen or anything else -- offense, defense, starting pitching," Lugo said. "These are my teammates, so I always feel for these guys. I know we can make the adjustment we need to make to be successful."

On paper, Lugo can be a key part of that adjustment. For more than two full years, the Mets kept him out of their rotation because they believed he was too valuable to them as a reliever. Given the Mets' other options at the time -- Jacob deGrom, Noah Syndergaard, Zack Wheeler and others -- the move made sense. Lugo rapidly developed into a true relief ace, as capable of serving as a three-inning fire extinguisher as he was of locking down a three-out save.

All throughout, Lugo made it clear that he'd rather start. All throughout, the Mets made it clear that they wanted him to relieve.

Only this month, in the midst of a 60-game season without Syndergaard, Wheeler or Marcus Stroman, did the Mets relent. Comfortable with their bullpen depth following the returns of Brad Brach and Jared Hughes, the Mets decided to give Lugo a chance -- with strong initial results. Relying on his usual five-pitch mix against the Yankees, Lugo allowed his only run on a Tyler Wade homer as he stretched out to his prescribed limit of 60 pitches.

Clearly fatiguing a bit in the fourth inning, Lugo loaded the bases on a hit and two walks, then lobbied for Mets manager Luis Rojas to leave him in the game. Rojas instead turned to Chasen Shreve, who retired Wade to keep the Mets within a run. Ultimately, the Mets fell short against Sánchez, rookie starter Deivi García and the Yankees' bullpen, but that didn't diminish Lugo's contribution. Through two starts, he's allowed one run over 6 2/3 innings, with 12 strikeouts.

"I foresee quality starts," Rojas said. "If he keeps stretching out, I see quality starts coming from him."

The problem has been what's happened to the bullpen in his absence. Earlier Sunday, Dellin Betances landed on the injured list due to right lat discomfort, robbing the Mets' relief corps of another back-end arm. Betances had been shaky even before the injury, as has Díaz since the Mets acquired him two years ago. Factor in some inconsistency from Jeurys Familia and Justin Wilson, and Rojas simply does not have a reliable path to 27 outs.

For two years, Lugo had papered over similar problems for the Mets' bullpen. The Mets can hope only that in the future, his contributions in the rotation outweigh his absence in relief.

"Today was a tough day," Rojas said. "Those two games were tough. … But that's the one ability that we've got to maintain, we've got to still be consistent that we bounce back from tough losses, tough games like this."