Since Jesus died long before the fall of the temple why would a story about him mention the temple?
One of the reasons Luke is thought to have be written then is due to the dating of Mark. And since Luke copied large swathes of Mark he obviously was a younger source . For various reasons an early date is rejected by most Bible scholars. It is mainly the fundamentalists that demand an early date:
The eclipse of the traditional attribution to Luke the companion of Paul has meant that an early date for the gospel is now rarely put forward.
[7] Most scholars date the composition of the combined work to around 80–90 AD, although some others suggest 90–110,
[16] and there is textual evidence (the conflicts between Western and Alexandrian manuscript families) that Luke–Acts was still being substantially revised well into the 2nd century.
[9]
Gospel of Luke
What you argue can be easily countered with much more persuasive evidence.
Internal evidence states that Luke wrote both the Gospel of Luke and the book of Acts [see Acts 1:1,2]. If the destruction of the temple (70 CE) had taken place before his writing of both books, then it would certainly have been mentioned. Yet, the book of Acts, which was written after the Gospel [see Acts 1:1,2], does not reach 70 CE! It follows the story of Paul's missionary journeys up until 63 CE, when Paul arrived in Rome [see Acts 28].
To determine the date of Luke's Gospel, one cannot simply date it according to Mark.
The most reliable way of dating Luke is to look at the internal evidence. Luke provides us with an account of Jesus' life, and the ministry of Holy Spirit during the early period of the Church. Luke sets all of this information in a framework of verifiable history and geography.
Here are just some of the historical markers that impact on the dating of
Luke's book of Acts.
1. The reign of Aretas of Damascus ( Acts 9:25, cf. 2 Cor.11:32)
2. The reign and death of Herod Agrippa 1 (Acts 12)
3. The famine under Claudius (Acts 11:28-30; 12:25)
4. The proconsulship of Sergius Paulus in Cyprus (Acts 13:7)
5. The expulsion of Jews from Rome under Claudius (Acts 18:2)
6. The proconsulship of Gallio in Achaia (Acts 18:12)
7. The reign of Herod Agrippa II, and marriage of his sister Drusilla to Felix (Acts 24:24; Acts 25:13-26:32)
8. The proconsulships of Felix and Festus (Acts 21:38; 23:24; 24:10,27)
9. The persecution under Nero.
Based on events that could be precisely determined, such as the death of Herod Agrippa (Acts 12:23) and St Paul's second appearance before Festus (26:32) Bishop Lightfoot has given the following reckoning of dates for fourteen events in the book of Acts.
1. The Ascension of Christ - 30 CE
2. Conversion of Saul - 34-36 CE
3. Paul's first visit to Jerusalem - 37,38 CE
4. Paul at Antioch - 44 CE
5. Paul's second Visit to Jerusalem - 45 CE
6. Paul's first missionary journey - 48 CE
7. The Great Council of Jerusalem - 51 CE
8. Paul's first visit to Corinth - 52 CE
9. Paul's fourth visit to Jerusalem - 54 CE
10. Paul leaves Ephesus - 57 CE
11. Paul's arrest in Jerusalem - 58 CE
12. Paul reaches Rome - 61 CE
13. Close of the 'Acts' - 63 CE
14. Paul is martyred - 67 CE
Conclusion: 'The abrupt conclusion of the narrative suggests a change of circumstances. Either the great fire of Rome, in 64 AD, or want of opportunity, or political discretion, or Luke's death, would account for the incompleteness of the record.' (Scroggie)