If we look in Bauer's Lexicon (BDAG), we see definition no. 1 of "dikaioo" is "to show justice, do justice, take up a cause" matches Thayer's definition no. 2:

            We can explain Paul's meaning using every one of the senses that Thayer's lexicon gives in definition no. 2, and all of the senses given in definition no. 1 from BDAG. Thayer:   (a) God willed to do one justice by the substitutionary death of Christ.  (b) God condemned us in Christ so that the penalty is paid. (c) We were punished through his sacrifice, BDAG: (e) God showed justice against our sin by the sacrifice of Christ; (f) God does justice to us in Christ; and (h) Christ takes up our cause before God by paying the penalty.   In Christ, we have justice done to ourselves.   We suffer justice by the substitute, and we are treated rightly when condemned through the divine substitute.

            However, notice that the second definition of this same word is to render a favorable verdict, justify, and acquit:[1]

            This second definition is the one that a multitude urges us to go by.   Yet did God render a favorable verdict for us?   By no means!   As sinners, we were found guilty.[2]   God will not justify the wicked in the sense of