Although the name was quite a common one, ancient tradition has usually identified our Luke with the Luke whom the apostle Paul mentions twice. Paul is an important character in The Acts of the Apostles, and our writer does seem to have travelled with Paul on some of his missionary journeys."
For this reason, it can be easily assumed that Paul had every opportunity to contribute to the book, and made a point to make sure it mentioned him often and in a good light. Luke traveled with Paul and, apparently, looked up to him. So, to say that Paul didn't have input is extremely naiive. There is absolutely no reason to think that he didn't.
Thank you for your ^above ^ observation.
Sorry I was Not more clear. By Paul Not having influence was meant that ALL Scripture is from: God - 2 Timothy 3:16-17
So, Paul was Not having influence over Luke to write down Paul's thoughts over God's thoughts.
Hope this is of some help.