Paul Anderson, who has undertaken a new quest for a new quest for the historical Jesus (i.e. using John), has published an article on a not unrelated topic of Lukan access to Johannine tradition. Here is a typical point:
John contains a good deal of primitive material, and thus the Johannine tradition would have been available to Luke as a gatherer of gospel material long before the finalization of either Gospel.
Away from this article but closer to others by Anderson, can John, with all its distinctive Christology and theology of a seemingly later period, really be used in the quest for the historical Jesus?