The view that Luke-Acts was written by Luke for Paul's trial is championed in this book entitled "Paul On Trial". Here is the Google Books description:
John W. Mauck Thomas Nelson Publishers, 2001 - Religion - 236 pages 0
Reviews
JOHN W. MAUCK provides an exciting new way of understanding the Book
of Acts. With great skill and powerful arguments, the author contends
that Acts was written primarily to defend Paul for his forthcoming
trial in Rome. After reading Mauck's volume, the read we will not only
gain a fuller understanding of Acts, but also obtain rock-solid
arguments for defending Christianity and understanding its Jewish
roots.
What's Inside: A fresh study of Acts as a legal "brief"
Insights gained from understanding of Roman law
Numerous Charts that outline Luke's "argument"
Recorded speeches viewed as "witness testimony"
A section-by-section review of all of Acts
A powerful apologetic defending the claims of Christianity
Endorsements:
"The book is a terrific addition to any lawyer's library. It makes the
Book of Acts come alive with new and useful insights." -- Samuel B.
Casey, Executive Director, Christian Legal Society
"It makes a constructive, fresh, and fascinating contribution to the
understanding of Acts." -- Dr. Donald Hagner, Author of Matthew in
WBC, Fuller Theological Seminary
I have not read the book but have long been fascinated by the idea. It does make one wonder if there were ever a time when anyone in a legal service would read such a huge document that probably filled a shelf in its original form!
So the book presents the case for it being a brief and to the degree you are convinced by the author is an indicator of the strength of the argument.