Correct: "Lawlessness" is the inverse of "lawFUL-ness" in an English context.
The assertion that it is directly associated with "righteousness" is readily seen, not only directly (such as the obvious first use), in Genesis 15:6, where then-Abram (before his renaming) "believed YHVH" and that was not only "accounted to him" as 'righteousness' (Hebrew word 'tzedekah') but serves as the very definition.
Variants of the Hebrew shoresh (3-letter root word) appear in the form of adjectives and nouns and even proper names (Zedekiah, Melek-tdedik or Melchizedek, et al) almost 500 times in Scripture, and comprise most of the Strong H666x series (H6662, first use describing Noach, through H6667. The first use of the form used by Judah to describe Tamar in Gen. 38:26 is also instructive.)
A tzadik is a righteous man, often translated literally as a scholar of His Word (the word most here know, but might get banned), one who "walks in His ways", and is "just" (generally the same root, by definition. HE is 'just'.) Examples in His Word abound.
Paul even spends a lot of ink on the concept, arguably much of the letter to the Romans, but chapter 7 in particular. Essentially, without His Written Instruction, we wouldn't even know what it MEANS to be "righteous." (or, in contrast, all the alternatives.)
I contend that Yahushua was not speaking Greek to an Aramaic and Hebrew-literate audience, and that the overwhelming preponderance of Scripture, and literally hundreds of uses in those various forms, make the best rendering of His warning in Matthew 7:21-23 of the 'Sermon on the Mount,"
"...And then will I profess unto them, I never knew you: depart from me, ye that work torah-less-ness." I.e., "who will not follow My instruction." After all, He also says,
"Why do you call me, 'Lord, LORD, and NOT do the things I say?" (Luke 6:46 - and the context there is critical.)