Why did Paul devote his life to preaching the Gospel to lost people?
Paul devoted his life to preaching the Gospel because Christ's cross paid the sin debt for all people, including the vilest, so the only remaining sin that brings eternal doom is rejecting the Gospel. He burned until his dying day to get the Gospel of salvation out to lost people.
Les explains that Christ's death was unique not merely as another crucifixion, but because the Creator God Himself took on human flesh and went to the cross. There God poured out all His wrath for sin, laying on Christ the sin of everyone from Adam to the last person who will live in time. Even the vilest lost people's sins are already atoned for and paid for. The only sin that brings eternal doom is rejecting the Gospel. That is why Paul burned until his dying day to get the Gospel of salvation out to lost people; if any of us gets a part of that, we would make a difference.