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The Lincoln in the alt universe was killed. That is Lincoln from Olivia's universe. He fell in love with Olivia, but when he realized that would never come to fruition because she loved Peter, he started falling for the other Olivia. So yes, he went over there when they closed the bridge between the two universes to be with her. Hope that helps =D

Thanks mesachick. I had a feeling it went something like that but I don't remember alt-Lincoln dying. I do remember Lincoln's crush on Olivia and missed all the episodes leading up to the final closing of the bridge.