There is actually a notably good reason for dating the gospel of Luke before the fall of Jerusalem, and that is that both Acts and Luke were written by the same author. It is thought by many that the author of both was Luke because of his companionship with Paul.
"The former account, indeed, I made concerning all things, O Theophilus, that Jesus began both to do and to teach,
2 till the day in which, having given command, through the Holy Spirit, to the apostles whom he did choose out, he was taken up,
3 to whom also he did present himself alive after his suffering, in many certain proofs, through forty days being seen by them, and speaking the things concerning the reign of God." (YLT)
The former account referenced in Acts 1:1 was the 3rd gospel account, and the same author wrote and sent it to the same individual (Theophilus) as was the book of Acts.
"Seeing that many did take in hand to set in order a narration of the matters that have been fully assured among us,
2 as they did deliver to us, who from the beginning became eye-witnesses, and officers of the Word, --
3 it seemed good also to me, having followed from the first after all things exactly, to write to thee in order, most noble Theophilus," (YLT)
The book of Acts then becomes a starting point to peg many of the other books of the NT, especially those of Paul's missionary journeys. Acts ends with the account of Paul's arrival and beginning of his two-year imprisonment in Rome in 61-62 A.D. waiting for trial (Acts 28:16-31). This places the book of Acts before the fall of Jerusalem in A.D. 70. We can conclude then that the "former account" sent to Theophilus - the gospel of Luke - was written before 61-62 A.D.
As there are no mention of the trial nor the outcome of the trial in Acts, it is probably safe to conclude that Acts was not written after Paul's trial. Therefore, the gospel of Luke could not have been written after Paul's trial either.
But other indications within the gospel of Luke are noteworthy. Excerpt from Dating The New Testament.com:
" Luke’s favorable attitude toward Rome points to a date before the persecution of Christians under Nero:
Roman soldiers are favorably addressed by John the Baptist, something mentioned only by Luke (Luke 3:14)
The account of the Centurion in Luke 7 is very favorable to the man, who “loves our nation” (7:5)
The Centurion Cornelius in Acts 10 is a favorable character who becomes a Christian
The Centurion and Roman commander in Acts 21-23 help Paul repeatedly
The Centurion guarding Paul on the ship while he is traveling to Rome is yet another favorably portrayed Roman soldier.
Paul is repeatedly treated with deference due to his Roman citizenship (Acts 16:37-38, 22:25-28)" Source: here
It is also telling that all of the gospels were prophesying the destruction of the temple, which meant the temple was still standing when the books were written. See Luke 21:6, Mat. 24:1; Mark 13:1. The temple prophesy was of an event that had not yet happened when the gospels were written. That fact alone puts their date before the fall of Jerusalem in A.D. 70.
Moreover, Acts could not have been written after the persecutions of Nero as no mention of those persecutions are included in the book. Nero began his persecutions after the fire of Rome in A.D. 64. Nor does Acts mention the martyrdom of James (A.D. 61-62), Paul (A.D. 64-65) nor Peter (AD 64-65).
Excerpt from the post "When were the gospels written and by whom" at Christian Apologetics & Research Ministry:
""At the earliest, Acts cannot have been written prior to the latest firm chronological marker recorded in the book - Festus's appointment as procurator (24:27), which, on the basis of independent sources, appears to have occurred between A.D. 55 and 59." Source: here
As the internal evidence shows that the third gospel was written by the same author of Acts, and before the book of Acts, and as the book of Acts can be shown to have been written after the appointment of Festus (55-59 A.D.) but before Paul's trial (61-62 AD), then the we can know that the gospel of Luke was written after 55 AD but before 61-62 AD.