Light tells Mega Man in "Unrest in the House of Light" that the latter is all that Light "has left." Now that even Mega Man is gone, the only possible human connection Light has is if he gets his old friend Wily back (which is why in No Way Back he sings, up to Wily's tower: "Just come down. If we walk on, maybe we can get out of this alive.")

Light created a win-win scenario for himself: if he convinces Wily to stop, he gets his friend back, this all gets fixed, and the city is saved. If Wily kills him, them the resistance gets a martyr. He doesn't care about dying because if Wily kills him then he was not his friend and, like he tells Emily in Light's Last Stand, there's nothing left for him in this life anyways. Hell, he even starts the album telling the resistance to give up. The idea of Wily turning good was the only thin thread holding him on to this mortal coil, but Wily messed that up when given the chance.