Luke could not have written the 2 books, as they were written somewhere between 80-110ce. Unless he lived to be 120 years old. You can not use a fable to prove it's own authenticity. You need historical, textural, and physical evidence. There is no historical, textural or physical evidence that supports the fact that someone named Luke ever wrote "Luke-Acts". Do you not read NT history? The Catholic Church decided the authors of the four gospels based upon their own assumptions. Spend a couple of years researching the history of the NT and you will find this out.
"Luke-Acts does not name its author. According to Church tradition this was Luke the evangelist, the companion of Paul, but while this view is still occasionally put forward the scholarly consensus emphasizes the many contradictions between Acts and the authentic Pauline letters. The most probable date for its composition is around 80-100 AD, and there is evidence that it was still being revised well into the 2nd century." WIKI
And it cites sources. Being tradition does not make it true. Santa Clause is tradition too, but not fact. The Epistle of Barnabas and the Shepherd Of Hermas were in the NT until the CC took them out. Being "in the NT" does not mean it is from God. It means the books included in the NT were chosen by the orthodox church to suit their own theology, much as each denomination picks which parts they will abide by and which parts they will not. I also have read the epistle of Barnabas, the Shepherd of Hermas,the Didache, most of the other gospels, Mary, Thomas, Peter, Phillip, Gospel Of Truth, Gospel Of Nicodemus, Infancy Gospel Of James, Gospel Of The Lord, and so many others. It's all scripture. What went into the NT was decided by the CC, not God. Being in the canon of the NT does not make it true. Men chose the books of the NT, not God. I put as much value in the Gospel Of Thomas as in any of the others. At least it names it's author.