We are told very little about Lazarus after his resurrection. We know that soon after his resurrection he continued to be a pain to the chief priests and scribes. People came to see him (John 12:9) and were converted because of his testimony. The priests even considered having Lazarus put to death because of his influence (John 12:10-11). However, there is no indication that anything came of this threat.
What about after this? Did Lazarus die again? Certainly, he did. We do not know when and we do not know the circumstances, but we can rest assured that his time to die came. When he died, his body was surely put in the ground to await the resurrection while his soul and spirit went to be with God to await the return of Christ. There is no reason to think that he was any different from the rest of us.