"Lazarus could not have been protected in the early period of the Jerusalem church's life by telling his story but not naming him. His story was too well known locally not to be easily identifiable as his however it was told. For Lazarus 'protective anonymity' had to take the form of his total absence from the story as it was publicly told. . . . If the raising of Lazarus was not only the remarkable event that John portrays but also such a key event in leading to Jesus' death, its absence from Mark -- and so, presumably, from the pre-Markan passion narrative -- is certainly puzzling. But the difficulty is removed when we recognize that the need for 'protective anonymity' in Lazarus's case would require his complete absence from any public telling of the passion narrative in the early Jerusalem church" - Richard Bauckham, Jesus and the Eyewitnesses: The Gospels as Eyewitness Testimony (Eerdmans, 2006), 196.The solution, it turns out, is not completely novel. According to William Baird, it was advanced at least as early as the 17th century, by Hugo Grotius (1583-1645), and subsequently adopted by others:
"As to the reason the other evangelists neglected to record the raising of Lazarus, Grotius adopts the hypothesis--popular with later apologetic exegetes--that Matthew, Mark, and Luke wanted to protect Lazarus and his family from the wrath of the high priests (12:10) and, therefore, kept the story secret. Years later, after their Gospels were written and the danger had passed, John was able safely to recount the miraculous event." - William Baird, History of New Testement Research, Vol. 1: From Deism to Tübingen (Minneapolis: Fortress, 1992), 11.Since Bauckham does not cite Grotius--or anyone else--in this regard, he may have come across the same solution independently. (After all, great minds think alike.) But Bauckham has a monograph on 16th century English apocalyptic thought, and he may have encountered Grotius in this connection.