Christ was raised in a glorified, or spiritual body:
So will it be with the resurrection of the dead. The body that is sown is perishable, it is raised imperishable; it is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power; it is sown a natural body, it is raised a spiritual body.
(1 Corinthians 15:42–44; NIV)
Christ's resurrected body, then, was something different than that of Lazarus:
Jesus said, "This sickness will not end in death. No, it is for God’s glory so that God’s Son may be glorified through it. ... Our friend Lazarus has fallen asleep."
(John 11:4, 11; NIV)
That is, Lazarus' illness was not "unto death", the separation of body and spirit; he was raised in a natural body, not having descended into Sheol.
Jesus, on the other hand, was the first to be resurrected:
Christ has indeed been raised from the dead, the firstfruits of those who have fallen asleep.
(1 Corinthians 15:20; NIV)
Paul's argument specifically refers to those who, following Christ, will be raised:
if we died with Christ, we believe that we will also live with him. For we know that since Christ was raised from the dead, he cannot die again.
Therefore he's referring in this passage to a resurrection like that of Jesus, not a raising back to natural life like Lazarus. That's why his argument doesn't apply to Lazarus.