Erik Bedard is supposed to return on Wednesday, which would bump Lincoln from the rotation. I'm not sure about Lincoln's viability as a starter in the long term, but there's no time like the present for the Pirates to see exactly what they have. Lincoln, James McDonald and Jason Grilli are arguably the Pirates who have done the most to improve their stock this season. The Bucs should go ahead and give Lincoln a shot and see what he does with it. With the depth the Pirates now have at Class AAA, Correia is almost completely superfluous, but if the Pirates wanted to keep him in the team, they could use him out of the bullpen.
There's no good reason I can see to leave Correia in the rotation. He isn't under contract beyond this year, and he has no real upside. On top of that, he isn't pitching well, with 14 strikeouts and 15 walks so far this season. Lincoln isn't likely to be a long-term answer in the rotation either, but he might be. He has also pitched very well this season, showing better velocity than in the past, and he had a quality start while stepping in for Bedard on Monday.