As for the link between the Pastorals and Lk.-Acts, in addition to the allusions in the Pastorals to persons or situations alluded to in the Acts (for which see the commentaries, and P. N. Harrison, The Problem of the Pastoral Epistles (1921), 93 ff.), note the following contacts: 1 Tim. v. 17 τιμή = material reward, cf. Acts xxviii. 10 πολλαῖς τιμαῖς ἐτίμησαν ἡμᾶς. 1 Tim. v. 18 ἄξιος ὁ ἐργάτης τοῦ μισθοῦ αὐτοῦ is the Lucan form (Lk. x. 7, τῦς τροφῆς αὐτοῦ, Matt. x. 10). 1 Tim. vi. 10 φιλαργυρἰα is a N.T. ἅπαξ λεγ.; Lk. xvi. 14, 2 Tim. iii. 2, both have φιλάργυρος (only here in N.T.). 1 Tim. vi. 17 ὑψηλοφρονεῖν (N.T. ἅπαξ λεγ.), cf. Lk. xvi. 15 τὸ έν άνθρώποις ὑψηλὀν (same context as φιλἀργυρος above), 1 Tim. vi. 18 πλουτεῖν ἐν ἔργοις καλοῖς ... ἀποθησαυρἰζοντες ἑαυτοῖς θεμέλιον κάλον εἰς τὸ μέλλον ἵνα ἐπιλάβωνται τῆς ὄντως ζωῆς, cf. Lk. xii. 21 οὕτως ὁ θησαυρίζων αὑτῷ καὶ μὺ εἰς θεὸν πλουτῶν and cf. Lk. xvi. 9 (moral from 'Dishonest Bailiff" parable). 2 Tim. ii. 12 εἰ ὑπομένομεν καὶ συμβασιλεύσομεν, cf. Lk. xxii. 28 f. ὐμεῖς δέ ἐστε οἱ διαμεμενηκότες μετ' ἐμοῦ ἐν τοῖς πειρασμοῖς μου‧ κἀγὼ διατἰθεμαι ἡμῖν ... βασιλεἰαν ... 2 Tim. ii. 19 ἔγνω κύριος τοῦς ὄντας αὐτοῦ καὶ ἀποστήτω ἀπὸ ἀδικίας πᾶς ὁ ὀνομάζων τὸ ὄνομα κυρίου, cf. Lk. xiii. 27 οὐκ οἶδα ὑμᾶς πόθεν ἐστέ‧ ἀπόστητε ἀπ' ἐμοῦ πάντες ἐργάται ἀδικίας (where Matt. vii. 23 has ἀποχωρεῖτε for ἀπόστητε. But admittedly Matt, also has, vii. 22, the allusion to ' naming the Lord' – κύριε, κύριε, οὐ τῷ σῷ ὀνόματι ἐπροφητεύσαμεν, κ.τ.λ.). 2 Tim. ii. 26 ἐζωγρηένοι,cf.Lk.v. 10 (only other N.T. occurrence of ζωγρεῖν ). 2 Tim. iv. 7 τὸν δρόμον τετέλεκα, cf. Acts xiii. 25 ὡς δὲ ἐπλήρου Ἰωάωης τὸν δρόμον, xx. 24 ὡς τελειώσω τὸν δρόμον μου. Indeed, 2 Tim. iv. 1-8 as a whole is reminiscent of the Pauline farewell in Acts xx. 17 ff., and the references to presbyter-episcopi in the Pastorals generally is like Acts xx; but of course it might be said that this is only because both passages are Pauline, not because both are Lucan! Note further that Maurer, in T.W.N.T. s.v. συνείδησις, remarks that in the post-Pauline N.T. writings, συνείδησις is almost always qualified by attributes (ἀγαθή, καθαρά, etc.). If this were generally true, it would provide to that extent a less clear connexion between the Acts and the Pastorals in particular; but in fact, while there are only two clear instances in Heb. and two in 1 Pet. (though the implications for one or two other passages point the same way), the others are from precisely our two groups of writings – the Acts (xxiii. 1, xxiv. 16) and the Pastorals (1 Tim. i. 5, 19, iii. 9) 2 Tim i. 3, ii. 22).
It is interesting that two recent works, not concerned with the present problem, both remark independently on connexions between the Pastorals and Luke: C. K. Barrett, Luke the Historian in Recent Study (1961), 62 f.; 'Luke ... shares the attitude of the Pastorals, though he is prevented by his subject-matter from uttering the explicit: O Timothy, guard the deposit ...'; J. C. O'Neill The Theology of Acts (1961), 176: 'The author of the Pastoral epistles has emphasized that Paul's defence before the Imperial court in Rome completed the preaching. In principle the Gentile mission was over Acts assumed the same view of Paul's martyrdom.'