Still working on my presentation on Luke's Gospel in Christchurch at the end of this week ...
One 'authorial intention' of Luke which we can be pretty clear about because he tell us it is his intention is to help Theophilus to be more sure of the things he already knows.
We also observe of Luke - to pick out one observation of many we could make - that his gospel, for one so close to Paul, is very light on understanding Jesus' death as an atoning sacrifice for sin. Indeed we could fairly readily argue that Paul's atonement theology is non-existent; that the necessity of Jesus being killed is that, according to Scripture, the Messiah must suffer.
Is it possible that Luke is negligent of atoning theology because this is not a matter of concern to Theophilus? If Theophilus, for example, is like the two centurions (of Luke 7 and Acts 10) then he is an upright man, generous to a fault, and keen as mustard on the God of the Jews but unsure whether truly welcomed into God's kingdom as a Gentile. By the end of Acts Theophilus should be in no doubt that the Messiah of the Jews is the Christ of the Gentiles, God's suffering servant for the world, who welcomes him into God's kingdom.
That is, Luke interprets the gospel of Jesus Christ for his primary audience.