In the last chapter of the fourth gospel, Jesus asked Peter three times, “Simon, son of Jonas, lovest thou me?” Jesus continued:
Jhn 21:18-19 Verily, verily, I say unto thee, When thou wast young, thou girdedst thyself, and walkedst whither thou wouldest: but when thou shalt be old, thou shalt stretch forth thy hands, and another shall gird thee, and carry [thee] whither thou wouldest not. This spake he, signifying by what death he should glorify God. And when he had spoken this, he saith unto him, Follow me.
TDWJL was following them during this conversation. Then Peter asked, “Lord, and what this man?” Why would Peter ask that if he was John the apostle? However, if he was Lazarus, it would make sense.
The context of the conversation between Peter and Jesus was dying. What Peter was asking about was Lazarus dying.
Jhn 21:22-23 Jesus saith unto him, If I will that he tarry till I come, what [is that] to thee? follow thou me. 23 Then went this saying abroad among the brethren, that that disciple should not die: yet Jesus said not unto him, He shall not die; but, If I will that he tarry till I come, what [is that] to thee?
Why would they think that Lazarus would not die?
Most likely they interpreted what Jesus said earlier that Lazarus would not die again after he was resurrected.
Jhn 11:25-26 Jesus said unto her, I am the resurrection, and the life: he that believeth in me, though he were dead, yet shall he live: 26 And whosoever liveth and believeth in me shall never die. Believest thou this?
I had previously thought Peter was just shifting the topic and diverting the attention to John by asking “Lord, and what this man?” But, if it was Lazarus, the context of the conversation then makes sense.