The phrase "the disciple whom Jesus loved" (ὁ μαθητὴς ὃν ἠγάπα ὁ Ἰησοῦς) or, in John 20:2; "the disciple beloved of Jesus" (μαθητὴν ὃν ἐφίλει ὁ Ἰησοῦς), is used six times in the Gospel of John, but in no other New Testament accounts of Jesus. John 21:24 states that the Gospel of John is based on the written testimony of this disciple. The tradition of the Church has been that this "Beloved Disciple" is John the Evangelist, one of the Twelve Disciples of Christ.
Some modern scholars have offered an alternative possibility: the Beloved Disciple is Lazarus of Bethany, based on John 11:5: "Now Jesus loved Martha and her sister and Lazarus", and John 11:3: "Therefore his sisters sent unto him, saying, Lord, behold, he whom you love is sick." Furthermore, the character of the Beloved Disciple is not mentioned before the raising of Lazarus (Lazarus being raised in John 11, while the Beloved Disciple is first mentioned in John 13).
However, there are many arguments against this hypothesis that Lazarus was the Beloved Disciple. Besides the strong argument of the silence of early Christian tradition regarding this theory, the Gospel of John itself seems to exclude this possibility. It does this in at least three ways:
1. The Chief Priests Sought to Kill Lazarus
After the account of the resurrection of Lazarus, while Jesus was in the home of Lazarus in Bethany, six days before the crucifixion, we are told the following in John 12:9-11:
"Now a great many of the Jews knew that He was there; and they came, not for Jesus’ sake only, but that they might also see Lazarus, whom He had raised from the dead. But the chief priests plotted to put Lazarus to death also, because on account of him many of the Jews went away and believed in Jesus."
If the "chief priests plotted to put Lazarus to death also", then not only would he want to keep a low profile and not go to Jerusalem for the feast of the Passover like Jesus, who was actually going to Jerusalem to be put to death, but Jesus Himself would likely not want Lazarus with Him to distract from His mission. Furthermore, Lazarus would have likely been arrested with Jesus in the Garden of Gethsemane, and he certainly would not want to be at the crucifixion where the Beloved Disciple is given the care of the Virgin Mary by Jesus from the Cross, surrounded by Jewish authorities and Roman soldiers. Also, the anonymous disciple of John 18:15 is usually interpreted as being the Beloved Disciple, who enjoys privileges that night because of his acquaintance with the High Priest, but this privileged disciple could not have been Lazarus, whom the chief priests sought to kill.
2. Lazarus Is Clearly Named, While the Beloved Disciple is Anonymous
Lazarus is named many times in John 11 and 12, but the Beloved Disciple is never named, even at the end of the Gospel when the author says that he is the Beloved Disciple. On the other hand, the Gospel's author is titled as that of John, who is truly never named in the Gospel. If the Beloved Disciple did not want to be named at the end of the Gospel, why would he indicate that he was Lazarus who was loved by Jesus in John 11 and 12 and then start being anonymous in John 13? Also, why is it so difficult to comprehend that Jesus could have loved someone as a friend outside the circle of His disciples who followed Him? Why so much secrecy behind this "secret disciple", only mentioned in two chapters of the New Testament which don't even refer to him as a disciple?
3. Lazarus is Never Referred to as a Disciple
In the Synoptic Gospels we are specifically told the Passover in the Upper Room was attended by Jesus with His Twelve Disciples (Mark 14:17), but we know the names of the twelve, and nowhere is Lazarus mentioned, therefore the Beloved Disciple who lay his head on the breast of Jesus is revealed here to be one of the Twelve. Furthermore, when Lazarus is named in John 11 and 12, he is never referred to as a disciple. And Lazarus is clearly absent from at least a portion of the first ten chapters of the Gospel of John, but we are told in John 21:24 of the Beloved Disciple that "we know his testimony is true" because he can testify of what he wrote, but this would require for him to be present at everything he wrote about, including the first ten chapters, but Lazarus was clearly in Bethany while Jesus was out preaching with His disciples. A disciple is a follower, but nowhere is it indicated that Lazarus followed Jesus around everywhere.
Conclusion
With this being said, it is clear from the Gospel of John that Lazarus is not the Beloved Disciple of the Gospel of John, which would have to be renamed the Gospel of Lazarus if he were, and if it was the Gospel of Lazarus, it would not be based on his eye-witness testimony, which is the one thing that we are told testifies to its truthfulness.
Some modern scholars have offered an alternative possibility: the Beloved Disciple is Lazarus of Bethany, based on John 11:5: "Now Jesus loved Martha and her sister and Lazarus", and John 11:3: "Therefore his sisters sent unto him, saying, Lord, behold, he whom you love is sick." Furthermore, the character of the Beloved Disciple is not mentioned before the raising of Lazarus (Lazarus being raised in John 11, while the Beloved Disciple is first mentioned in John 13).
However, there are many arguments against this hypothesis that Lazarus was the Beloved Disciple. Besides the strong argument of the silence of early Christian tradition regarding this theory, the Gospel of John itself seems to exclude this possibility. It does this in at least three ways:
1. The Chief Priests Sought to Kill Lazarus
After the account of the resurrection of Lazarus, while Jesus was in the home of Lazarus in Bethany, six days before the crucifixion, we are told the following in John 12:9-11:
"Now a great many of the Jews knew that He was there; and they came, not for Jesus’ sake only, but that they might also see Lazarus, whom He had raised from the dead. But the chief priests plotted to put Lazarus to death also, because on account of him many of the Jews went away and believed in Jesus."
If the "chief priests plotted to put Lazarus to death also", then not only would he want to keep a low profile and not go to Jerusalem for the feast of the Passover like Jesus, who was actually going to Jerusalem to be put to death, but Jesus Himself would likely not want Lazarus with Him to distract from His mission. Furthermore, Lazarus would have likely been arrested with Jesus in the Garden of Gethsemane, and he certainly would not want to be at the crucifixion where the Beloved Disciple is given the care of the Virgin Mary by Jesus from the Cross, surrounded by Jewish authorities and Roman soldiers. Also, the anonymous disciple of John 18:15 is usually interpreted as being the Beloved Disciple, who enjoys privileges that night because of his acquaintance with the High Priest, but this privileged disciple could not have been Lazarus, whom the chief priests sought to kill.
2. Lazarus Is Clearly Named, While the Beloved Disciple is Anonymous
Lazarus is named many times in John 11 and 12, but the Beloved Disciple is never named, even at the end of the Gospel when the author says that he is the Beloved Disciple. On the other hand, the Gospel's author is titled as that of John, who is truly never named in the Gospel. If the Beloved Disciple did not want to be named at the end of the Gospel, why would he indicate that he was Lazarus who was loved by Jesus in John 11 and 12 and then start being anonymous in John 13? Also, why is it so difficult to comprehend that Jesus could have loved someone as a friend outside the circle of His disciples who followed Him? Why so much secrecy behind this "secret disciple", only mentioned in two chapters of the New Testament which don't even refer to him as a disciple?
3. Lazarus is Never Referred to as a Disciple
In the Synoptic Gospels we are specifically told the Passover in the Upper Room was attended by Jesus with His Twelve Disciples (Mark 14:17), but we know the names of the twelve, and nowhere is Lazarus mentioned, therefore the Beloved Disciple who lay his head on the breast of Jesus is revealed here to be one of the Twelve. Furthermore, when Lazarus is named in John 11 and 12, he is never referred to as a disciple. And Lazarus is clearly absent from at least a portion of the first ten chapters of the Gospel of John, but we are told in John 21:24 of the Beloved Disciple that "we know his testimony is true" because he can testify of what he wrote, but this would require for him to be present at everything he wrote about, including the first ten chapters, but Lazarus was clearly in Bethany while Jesus was out preaching with His disciples. A disciple is a follower, but nowhere is it indicated that Lazarus followed Jesus around everywhere.
Conclusion
With this being said, it is clear from the Gospel of John that Lazarus is not the Beloved Disciple of the Gospel of John, which would have to be renamed the Gospel of Lazarus if he were, and if it was the Gospel of Lazarus, it would not be based on his eye-witness testimony, which is the one thing that we are told testifies to its truthfulness.