Well, we would have to look at each case. But let's say that they are all references to the Law of Moses. Surely, you must realize that this in no way necessitates that we have to interpret any New Testament references to "lawlessness" in the same way.
Let's take a look.
Matt 7:23 And then will I profess unto them, I never knew you: depart from me, ye that work iniquity.
Matt 13:41 The Son of man shall send forth his angels, and they shall gather out of his kingdom all things that offend, and them which do iniquity;
Matt 23:28 Even so ye also outwardly appear righteous unto men, but within ye are full of hypocrisy and iniquity.
Matt 24:12 And because iniquity shall abound, the love of many shall wax cold.
Rom 4:7 Saying, Blessed are they whose iniquities are forgiven, and whose sins are covered.
Rom 6:19 I speak after the manner of men because of the infirmity of your flesh: for as ye have yielded your members servants to uncleanness and to iniquity unto iniquity; even so now yield your members servants to righteousness unto holiness.
2Cor 6:14 Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?
2Thess 2:7 For the mystery of iniquity doth already work: only he who now letteth will let, until he be taken out of the way.
Titus 2:14 Who gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works.
Heb 1:9 Thou hast loved righteousness, and hated iniquity; therefore God, even thy God, hath anointed thee with the oil of gladness above thy fellows.
Heb 8:12 For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more.
Heb 10:17 And their sins and iniquities will I remember no more.
1John 3:4 Whosoever committeth sin transgresseth also the law: for sin is the transgression of the law.
Now shall we just focus on what Paul said and in it's context?
He says that he had not known sin but by the law. And respect to it he says we have been made free from sin and have become slaves to righteousness wherein before we were slaves to iniquity. And iniquity is being said in respect to sin which is known by the law. So you think John and Paul were of different spirits and disagreed?
Rom 6:18 Being then made free from sin, ye became the servants of righteousness.
Rom 6:19 I speak after the manner of men because of the infirmity of your flesh: for as ye have yielded your members servants to uncleanness and to iniquity unto iniquity; even so now yield your members servants to righteousness unto holiness.
Rom 6:20 For when ye were the servants of sin, ye were free from righteousness.
Rom 7:7 What shall we say then? Is the law sin? God forbid. Nay, I had not known sin, but by the law: for I had not known lust, except the law had said, Thou shalt not covet.
Maybe look to how Jesus used the word next or the writer of Hebrews?