Jesus Christ is Lord
In each instance the word translated "Lord" is κυρίου:
14 But their minds were hardened, for until this very day the same veil remains on the reading of the old covenant— it not being unveiled because it passes-away in Christ. 15 Indeed, until today whenever Moses is being read, a veil lies on their heart. 16 But whenever it turns to the Lord, the veil is taken-away. 17 Now the Lord is the Spirit, and where the Spirit of the Lord is, there is freedom! (2 Corinthains 3 DLNT)
14 ἀλλὰ ἐπωρώθη τὰ νοήματα αὐτῶν. ἄχρι γὰρ τῆς σήμερον ἡμέρας τὸ αὐτὸ κάλυμμα ἐπὶ τῇ ἀναγνώσει τῆς παλαιᾶς διαθήκης μένει μὴ ἀνακαλυπτόμενον, ὅτι ἐν Χριστῷ καταργεῖται
15 ἀλλ' ἕως σήμερον ἡνίκα ἂν ἀναγινώσκηται Μωϋσῆς κάλυμμα ἐπὶ τὴν καρδίαν αὐτῶν κεῖται 16 ἡνίκα δὲ ἐὰν ἐπιστρέψῃ πρὸς κύριον, περιαιρεῖται τὸ κάλυμμα 17 ὁ δὲ κύριος τὸ πνεῦμά ἐστιν: οὗ δὲ τὸ πνεῦμα κυρίου, ἐλευθερία (NA26)
On κυρίου Thayer's says: "ὁ (properly, an adjective κύριος, κυρία, κύριον, also of two term.; properly equivalent to ὁ ἔχων κῦρος, having power or authority) (from Pindar down), he to whom a person or thing belongs, about which he has the power of deciding; master, lord."
Paul earlier affirmed, for him and other Christians, there is one Lord:
yet for us there is one God, the Father, from whom are all things and for whom we exist, and one Lord, Jesus Christ, through whom are all things and through whom we exist.
(1 Corinthians 8:6 ESV)
The veil Paul refers to is drawn from Moses covering his face as recorded in Exodus:
29 When Moses came down from Mount Sinai, with the two tablets of the testimony in his hand as he came down from the mountain, Moses did not know that the skin of his face shone because he had been talking with God.[d] 30 Aaron and all the people of Israel saw Moses, and behold, the skin of his face shone, and they were afraid to come near him. 31 But Moses called to them, and Aaron and all the leaders of the congregation returned to him, and Moses talked with them. 32 Afterward all the people of Israel came near, and he commanded them all that the LORD had spoken with him in Mount Sinai. 33 And when Moses had finished speaking with them, he put a veil over his face.
[d.] Exodus 34:29 Hebrew him
34 Whenever Moses went in before the LORD to speak with him, he would remove the veil, until he came out. And when he came out and told the people of Israel what he was commanded, 35 the people of Israel would see the face of Moses, that the skin of Moses' face was shining. And Moses would put the veil over his face again, until he went in to speak with him. (Exodus 34 ESV)
Paul applies the veil in two ways:
- Unveiled: Moses face when speaking
- Veiled: The Israelites heart after hearing
The first is taken from Exodus: whenever Moses is speaking his face is unveiled. Paul's second application is a midrash: he puts the veil not on Moses, but on the Israelites who cover their heart.
The Believer's Unveiled Face
Paul begins by comparing the Christian to Moses:
Since we have such a hope, we are very bold, not like Moses, who would put a veil over his face...(2 Corinthians 3:12-13 ESV)
Unlike Moses who put on the veil after speaking to the Israelites, Paul says the Christian does not need to cover their face. This follows what Paul will later say to the church in Rome:
For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek. (Romans 1:16 ESV)
Paul says the Christian never puts on a veil:
Now the Lord [d] is the Spirit, and where the Spirit of the Lord is, there is freedom. And we all, with unveiled face, beholding the glory of the Lord,[e] (2 Corinthians 3:17-18 ESV)
[d.] 2 Corinthians 3:17 Or this Lord [e.] 2 Corinthians 3:18 Or reflecting the glory of the Lord
Having the Spirit of the Lord is freedom. He does not need to ever cover his face before or after speaking about Jesus Christ. In fact, no Christian need be ashamed or afraid because the Gospel is the glory of Christ:
In their case the god of this world has blinded the minds of the unbelievers, to keep them from seeing the light of the gospel of the glory of Christ, who is the image of God.
(2 Corinthians 4:4 ESV)
The Israelites Veil
The Disciples Literal New Testament offers this translation for verse 16:
But whenever it turns to the Lord, the veil is taken-away.
ἡνίκα δὲ ἐὰν ἐπιστρέψῃ πρὸς κύριον, περιαιρεῖται τὸ κάλυμμα
A literal reading would be "whenever however if shall have turned to Lord, is taken away the veil." As some commentators such as Ellicott note, Paul is saying if Israel turns to the Lord (literally "Lord"). Here the reference is to Exodus 34:31 in the LXX:
And Moyses called them, and Aaron and all the rulers of the congregation turned to him, and Moyses spoke to them. (LXX NETS)
καὶ ἐκάλεσεν αὐτοὺς Μωυσῆς καὶ ἐπεστράφησαν πρὸς αὐτὸν Ααρων καὶ πάντες οἱ ἄρχοντες τῆς συναγωγῆς καὶ ἐλάλησεν αὐτοῗς Μωυσῆς
Paul's point is if the Jewish people turn back to the gospel of the glory of Christ, the veil is taken away. He is pointing to Aaron and the rulers who turned back, saw Moses unveiled face reflecting the glory of the LORD, and listened to what he said. If they do not turn back, they keep the veil on their hearts where, according to Paul, it has been ever since Moses spoke to them.
Obviously Paul's statements about the Israelites in general have specific application at the individual level, whether Jewish or Gentile, but the passage addresses the general, not the specific.