"The Synoptic Problem becomes significant here:
Did John (or an interpolator) have access to Luke, or did Luke have access to John in writing Luke/Acts?John appears to take great pains to maintain independance from the Synoptic Gospels, in regard to both style and content. He appears only to make direct reference to Mark, and makes no effort to use or even confirm the 'Q' material from Luke and Matthew.
Yet a handful of peculiar clauses and expressions are shared between John and Luke: Why would John insert these phrases into his own Gospel in such a random manner, with no apparent purpose?
If Luke made Use of John...
But what if Luke was composed after John, and had access to it, or at least to traditions originating in the Johannine community? In fact, a remarkable number of passages in Luke appear to depend upon the Johannine tradition, such as Luke 9:55-56 (cf. Jn 3:16-17), Luke 10:1-24, especially 10:2-3 (cf. Jn 4:35-36), and 10:21-22 (cf. Jn 5:25-27, 8:42-43, 10:27-30 etc.), Luke 11:29-36 (cf. Jn 2:18 etc.), and Luke 12:14 (cf. Jn 8:15-16).
The parallels between Luke 11:20 (cf. Jn 8:6,8!), and especially Luke 21:37-38/Acts 5:21 (cf. Jn 7:53-8:2) become now become more explicable. Luke takes the Johannine traditions and works them into his compilation of previous written and oral tradition, modifying them extensively just as he has done with Mark. Luke openly confesses as much, in the first 4 verses (Luke 1:1-4).
Most importantly, now the amazing parallel in Luke 21:37-38 takes on a new meaning: Besides providing the authoritative background for Luke's following material, Luke carefully preserves together material from both sides of the apparent 'seam' between John 8:1 and 8:2. Could Luke have done this to prevent or combat the physical cutting apart of this seam and removal of John 8:2-11?
If so, Luke would become the earliest known witness to the authenticity of the Pericope de Adultera!