DIKAIOW and BDAG Greek-English Lexicon

For DIKAIOW, Bauer, Danker, Arndt and Gingrich (BDAG) state that the potential senses of this word are (1) to take up a legal cause, show justice, do justice, take up a cause; (2) to render a favorable verdict, vindicate (Luke 7:35; 16:15); (3) be acquitted, be pronounced or treated as righteous and thereby become DIKAIOS (Galatians 2:16ff); (4) Concerning the view that DIAKAIOW can mean "make righteous," BDAG says the following:

"For the view (held since Chrysostom) that [DIKAIOW]
in these [Romans 3:24; 8:30, 33, Galatians 3:8] and
other pass[ages] means 'make upright' s[ee]
Goodsp[eed], Probs. 143-46, JBL 73, '54, 86-91."

LSJ observes that DIKAIOW may denote "set right, proved, tested, hold or deem right, claim or demand as a right, pronounce judgment, do a man right, chastise, punish, pass sentence on, have right done one, and pronounce and treat as righteous, justify, vindicate" (Exodus 23:7; Jeremiah 3:11; Luke 7:35; 16:15).

Louw and Nida's Greek-English Lexicon of the New
Testament Based on Semantic Domains observes that
DIKAIOW has the semantic range:

(a) to put right with
(b) show to be right
(c) acquit
(d) set free
(e) obey righteous commands

There are some interesting comments made regarding the forensic interpretation of DIKAIOW in semantic domain 34.46 of Louw and Nida. They basically argue that Paul stresses the covenant relationship between God and Christians as opposed to legal aspects of forensic judgment when he employs DIKAIOW. Under semantic domain 56.34, they also expand on the significance of the potential denotation, "acquit" by including the definition: "the act of clearing someone of transgression." See Acts 13:38; Romans 5:16, 18.

Finally, TDNT (2:215) states:

"For Paul the word DIKAIOUN does not suggest the
infusion of moral qualities, a justum efficere in the
sense of creation of right conduct. It implies the
justification of the ungodly who believe, on the basis
of the justifying action of God in the death and
resurrection of Christ."