Ben Witherington has advocated the case, concerning the authorship of the pastorals, that “the voice is the voice of Paul, but the hand is the hand of Luke” suggesting that “these letters reflect a combination of Pauline and Lukan style.” C. F. D. Moule put it this way: “Luke wrote all three Pastoral Epistles. But he wrote them during Paul’s lifetime, at Paul’s behest, and in part (but only in part), at Paul’s dictation.”
This should give us cause for serious reflection. What is the apparent relationship here? Either the writer of the Pastoral Epistles is aware of the Acts, or vice versa? Or is there a connection in authorship? If the plausibility of the “we” passages in Acts is historically probable, chronologically, it seems possible that Luke and Paul were together long enough for Luke to have acted as an amanuensis for Paul. However, the proposal of Lukan influence in these letters has been seriously critiqued by scholars, such as I. H. Marshall who notes, “The hypothesis of a Lucan origin for the PE should be dropped from consideration.” Thus, in response to Steph's question, my mental jury is still out on the possible and/or probable connections between these documents and authors. I think it's possible, but the question remains: Is it likely?
 Witherington, A Socio-Rhetorical Commentary on Titus, 1-2 Timothy and 1-3 John, pg. 60
 C. F. D. Moule, “The Problem of the Pastoral Epistles: A Reappraisal,” Bulletin of John Rylands Library 47 (1965): 434. Quoted in Witherington, A Socio-Rhetorical Commentary on Titus, 1-2 Timothy and 1-3 John, pg. 58
 Marshall, The Pastoral Epistles, pg. 88