I would not return to so well-worn a theme, were it not that editors like Dr Leaf (ad loc.) still state that there is nothing in the language of the last line to hinder us from taking it either of the litigant or of the judge.
Scholars have fixed their attention so closely on the words δίκην εἴποι that they have completely overlooked the qualifying ἰθύντατα. In modern courts of law we do not expect to hear the straightest statement of a case from advocates, but rather from the judge. The ancient Greek would never dream of expecting a litigant to give a straight statement of his case. The following passages will show that ἰθύς, ἰθύνειν, εὐθύνειν, ὀρθός are always applied to a judge (the converse σκολιός being used of unjust judges). The metaphor is from the carpenter’s rule (cf. ἐπὶ στάθμην ἰθύνειν Od. V. 245).
Pind. Pyth. IV. 152 καὶ θρόνος, ᾦ ποτε ἐγκαθίζων Κρηθεΐδας ἱππόταις εὔθυνε λαοῖς δίκας.
Solon 3. 36 εὐθύνων σκολιὰς δίκας.
Il. XVI. 387 οἳ βίῃ εἰν ἀγορῇ σκολιὰς κρίνωσι θέμιστας.
Hesiod Opp. 221 σκολιῇς δε δίκῃς κρίνωσι θέμιστας.
Hes. Opp. 222
Arist. Rhet. I. 1 οὐ γὰρ δεῖ τὸν δικαστὴν διαστρέφειν εἰς ὀργὴν προάγοντας ἢ φθόνον ἢ ἔλεον· ὅμοιον γάρ κἂν εἴ τις, ᾧ μέλλει χρῆσθαι κανόνι, τοῦτον ποιήσειε στρεβλόν.
Pind. Pyth. XI. 15 ὀρθοδίκαν γᾶς ὀμφαλόν.