"If Irenaeus was being truthful [in what he said about Polycarp], similar to Clement of Rome, Polycarp's writings become very important, since he personally knew and followed one of Jesus' closest disciples who was one of the three major leaders of the Jerusalem Church: John. However, without an ability to know and with only Irenaeus linking Polycarp to John, we may only assign Polycarp a rating of possible, in terms of preserving apostolic teachings pertaining to the resurrection of Jesus." (p. 256)
Let's begin with Irenaeus, since he's the only source Licona cites. Is there any reason to distrust him on the issue of Polycarp's relationship with John? Not that I'm aware of. I've read everything Irenaeus wrote. I've studied his writings in various contexts for years. I've read many scholars' comments about him. What I've read about Irenaeus' character in Eric Osborn's Irenaeus Of Lyons (New York: Cambridge University Press, 2005), for example, suggests to me that he was sufficiently honest and careful to warrant our trusting what he reported about Polycarp. Osborn writes:
"Eusebius' claim that Irenaeus was a peacemaker in name and nature (H.E. 5.24.18) is not simply a play on words but a fact borne out by Irenaeus' life and work (H.E. 5.23-5). His irenic approach shows that his objection to heresies on matters of faith had little to do with a struggle for power....Even on matters of faith, elsewhere he prays for his adversaries whom he loves more than they love themselves (3.25.7)....Irenaeus follows Justin as a lover of truth....As a ruthless empiricist, he constantly appeals to evidence and demands respect for facts....The evidence of facts must be accepted without argument, whether these facts are proclaimed by scripture or observed in the world....Irenaeus would not raise harmful rumour for the sake of scoring a point against his opponents." (pp. 5, 18, 203, n. 13 on p. 240)
Think about some of the characteristics of Irenaeus' comments about Polycarp. He mentions Polycarp's relationship with John on multiple occasions, in a wide variety of contexts. He cites the connection between Polycarp and John when arguing against heretics (Against Heresies, 3:3:4), in his letter against Florinus (Fragments, 2), and in his letter against Victor (Fragments, 3). In every one of those instances, he's appealing to Polycarp against his opponents. That would be a risky move if he was lying. And the apparent failure of any of his opponents to expose the lie in any way that's extant in our historical record would be hard to explain. Many people, and not just Irenaeus' opponents, would have had an interest in stating and popularizing the fact that Polycarp wasn't actually a disciple of the apostles, if in fact he wasn't.
In the first two passages mentioned above, Irenaeus adds some comments about how his assessment of Polycarp can be verified. He notes that "To these things all the Asiatic Churches testify, as do also those men who have succeeded Polycarp down to the present time" (Against Heresies, 3:3:4). It doesn't sound like Irenaeus was the only one claiming that Polycarp was a disciple of John. It sounds like other sources, including Polycarp's own church and his own successors in the bishopric, were saying the same thing. In his letter to Florinus, Irenaeus is addressing a childhood acquaintance. He appeals to the fact that Florinus also knew Polycarp when he and Irenaeus were in their youth. Why would Irenaeus not only lie and not only use that lie in a public dispute with somebody who was in a position to easily expose the lie, but even explicitly and repeatedly remind that individual about how he's in a position to refute the falsehood? In his letter to Florinus, Irenaeus reminds him that he had known Polycarp as well and repeatedly mentions Polycarp's status as a disciple of the apostles.
And it wouldn't make sense to argue that Irenaeus was honestly mistaken. Read what he says about the nature of his memories of Polycarp, especially in his letter to Florinus. He mentions many details, and he comments on how Polycarp would often discuss his relationship with the apostles. The idea that Irenaeus so frequently misunderstood Polycarp or misremembered what he said is unlikely. Did he also misunderstand or misremember the testimony of the Asian churches and Polycarp's successors, who, according to Irenaeus, were also testifying to the fact that Polycarp was a disciple of the apostles?
I see no reason to doubt Irenaeus' testimony about Polycarp's status as one of the apostles' disciples. I see much reason to trust his testimony.
And Licona seems to have overlooked some other sources we have.
Tertullian not only refers to Polycarp as a disciple of John, but even says that the claim can be verified in the records of the church of Smyrna (The Prescription Against Heretics, 32).
Eusebius, who had access to many documents no longer extant, refers to Polycarp's status as a disciple of the apostles as if it's accepted by him and as if he doesn't expect to have to defend the claim against any challenges (Church History, 3:36). He was willing to dispute Irenaeus' claim that Papias was a disciple of John (Church History, 3:39), but he accepts Polycarp's status as a disciple of the apostles.
Jerome likewise affirms Polycarp's relationship with the apostles and says nothing of any dispute on the matter (Lives Of Illustrious Men, 17). I'm not aware of any ancient source who disputed what Irenaeus reported about Polycarp.
I only noticed one reference to Justin Martyr in Licona's book, a brief reference in a footnote (n. 7 on p. 469). In the second part of this review, I discussed some of my reasons for thinking that Licona should have given more attention to Justin's material. I want to expand on that point now.
One of the most significant passages in Justin relevant to Jesus' resurrection is cited by Licona in the footnote I've referred to above. But Licona doesn't say much about the passage.
It's seldom noted that Matthew's claim that the Jewish leaders accused Jesus' disciples of stealing His body from its tomb is corroborated by a passage in Justin in which he seems to quote from a Jewish source on the subject. In section 108 of his Dialogue With Trypho, Justin seems to cite a Jewish document or tradition, in which Jesus is referred to as a "deceiver" and reference is made to Jesus as Him "whom we crucified", apparently speaking from the perspective of non-Christian Jews ("we"). This passage in Justin contains multiple details not found in Matthew's gospel. For example, Michael Slusser's edition of Justin has him referring to how the Jews "chose certain men by vote and sent them throughout the whole civilized world" in order to argue against Christianity, including by accusing the disciples of stealing the body (Dialogue With Trypho [Washington, D.C.: The Catholic University Of America Press, 2003], p. 162). It's not as though people would have been dependent solely on Matthew for information on such subjects. Justin had more than Matthew's account to go by. And he seems to be quoting some sort of Jewish document or tradition.
Justin addresses a lot of issues that Licona discusses in his book. We find in Justin many indications of early Jewish familiarity with the gospels (Dialogue With Trypho, 10) and early Jewish belief about issues like Jesus' crucifixion (32) and His performance of miracles (69). Both Justin and his Jewish opponents argue on the basis of a historical reading of the gospels, which tells us how both early Christians and early Jews viewed the genre of those documents.
How significant is Justin's Dialogue With Trypho as a response to Jewish argumentation? How likely is it that Jewish arguments are actually reflected in what he writes? Justin is familiar with many Jewish responses to Christianity, as his interactions with their scripture interpretations, for example, demonstrate. He "shows acquaintance with rabbinical discussions" (Michael Slusser, ed., Dialogue With Trypho [Washington, D.C.: The Catholic University Of America Press, 2003], n. 9 on p. 33). Bruce Chilton writes that Justin "appears to adapt motifs of Judaism", and Rebecca Lyman comments that Justin "is aware of Samaritan customs as well as some patterns of rabbinic exegesis" (in Sara Parvis and Paul Foster, edd., Justin Martyr And His Worlds [Minneapolis, Minnesota: Fortress Press, 2007], pp. 83, 163). Passages like the ones I've discussed above in Justin's Dialogue With Trypho demonstrate that he wasn't just repeating what he read in the New Testament documents. He's aware of Jewish arguments outside of those reflected in the New Testament, and he's aware of post-apostolic developments in Judaism. His willingness to compose a work as lengthy as his Dialogue With Trypho tells us something about his interest in Jewish arguments against Christianity.