‘But whenever it shall turn to the Lord, the veil is taken away.'
Here we have to interpret ‘it'. So, it could mean ‘but whenever the heart (referring back to 2 Corinthians 3:15) of a man turns to the Lord', or ‘whenever there is a turning to the Lord' or ‘whenever a person turns to the Lord', the veil is taken away. The overall idea is the same and the verb gives the impression of the swiftness of it. The person looks and lives.
‘To the Lord.' Taken in context we would expect ‘the Lord' to mean Jesus Christ (compare 2 Corinthians 1:2-3; 2Co 1:14; 2 Corinthians 4:5; 2 Corinthians 4:10; 2 Corinthians 4:14; 2 Corinthians 11:17 and see 1 Corinthians 8:6 and Paul's regular unquestionable references to Jesus Christ in that letter as ‘the Lord' (1Co 2:8; 1 Corinthians 4:5; 1 Corinthians 6:14; 1Co 10:21; 1 Corinthians 11:20; 1 Corinthians 11:26-27; 1 Corinthians 11:29; 1Co 12:3; 1 Corinthians 12:5; 1 Corinthians 15:47). Then the idea would be the general one that all men have a veil over their hearts, and when they turn to the Lord Jesus Christ it results in the veil being taken away (see 2 Corinthians 4:4).
But strictly the veil is in context said to be over the hearts of those who hear ‘Moses'. So alternately it may mean ‘whenever anyone (who is listening to the reading of the Law) turns to the Lord the veil is taken away' signifying those who listen to the reading of ‘Moses' (2 Corinthians 3:15). It is then declaring that any such who genuinely reach out to the Lord, here referring back to the Lord of the Old Testament, (Who however is Jesus Christ) will in that be enlightened, with the necessary result that they turn to Jesus Christ. The corollary is that those who cling to Moses are still veiled.