If there was no one resurrected before Christ, then what about the raising of Lazarus? Is his resurrection different because he was still subject to death again?
According to Scripture, Jesus was the first person to be resurrected (1Cor 15:20), and you offered part of the answer in your question for why we cannot consider Lazarus (or any of the other people Jesus raised from the dead) to have preceded Jesus in resurrection. Resurrection as it is described in Scripture requires two elements, neither of which were present for Lazarus nor the other people raised from the dead during Jesus' ministry on Earth.
First, as you say each person Jesus raised prior to his own resurrection was subject to death again at some later point. A true resurrection is one that returns a person to a permanent state of new life, one in which the person is never to be subjected to death again (see Heb 9:27; Rom 6:8-9; 1Cor 15:54, etc.). When Lazarus died, he didn't face the moment of judgment nor did he escape death forever. Once Jesus raised him from the dead, he continued in his Earthly life and eventually faced his true death and judgment.
Secondly, resurrection is a transformation into a new body, one that is fundamentally different than the one that preceded it. Paul describes the nature of true resurrection at length in 1Cor 15, where he teaches that the body of a resurrected believer is a new, better form than the previous body. When Lazarus and the others like him were brought back to life, they merely returned to their existing, corrupt body. This is why they had to die again, because the putting away of our present body is a necessary prerequisite to receiving a new body.
If we assume that Lazarus was a believer in Jesus Christ (probably a safe assumption), then we can be sure he will one day be resurrected into a new body (together with all believers) and will live eternally with Christ. His earlier "brush with death" was not his resurrection moment, but simply an opportunity or God to display His power over death. The account in John 11 makes clear that God intended for Lazarus to die temporarily so that he could be raised again (John 11:4).