Kassios,
If you are right, then many references require explanation. Please start by correcting this entry for Dice (Dike), the Greek goddess:
"DICE, the personification of justice, was, according to Hesiod, a daughter of Zeus and Themis, and the sister of Eunomia and Eirene. She was considered as one of the Horae; she watched the deeds of man and approached the throne of Zeus with lamentations whenever a judge violated justice. She was the enemy of all falsehood and the protectress of a wise administration of justice; and Hesychia, that is, tranquillity of mind, was her daughter. She is frequently called the attendant or councilor of Zeus. In the tragedians, Dice appears as a divinity who severely punishes all wrong, watches over the maintenance of justice, and pierces the hearts of the unjust with the sword made for her by Aesa. In this capacity she is closely connected with the Erinnyes, though her business is not only to punish injustice, but also to reward virtue. The idea of Dice as justice personified is most perfectly developed in the dramas of Sophocles and Euripides. She was represented on the chest of Cypselus as a handsome goddess, dragging Adicia (Injustice) with one hand, while in the other she held a staff with which she beat her."
http://ancientlibrary.com/smith-bio/1008.html
Also, please revise the following statement so that it will be factually correct:
THE HORAE
The Horae are the goddesses of the seasons and the orderly procession of things in general. They are also the collective personification of justice. Hesiod, who saw them as givers of the law, justice and peace, gave them the names Eunomia (Discipline), Dice (Justice) and Eirene (Peace). At Athens two of the Horae, were called Thallo and Carpo, and to the Athenians, represented the budding and maturity of growing things. As a result, Thallo became the protectress of youth.
http://www.amystical1.com/greekgodsgoddesses.htm
If you still strongly disagree, please correct the following pages also.
http://mail.tku.edu.tw/kiss7445/KissHomePage/Literature-Arts/Note-98-3.htmhttp://theoi.com/Encyc_D.htmlhttp://www.answers.com/topic/horae
All this tells me that the lexicon you cited that listed "right" as the second meaning of the word dikê is perfectly reasonable. But translating LAODIKE as the "right of the people" would be misleading. It's the sense of "right" ("the way of mortals" in definition A) that is the true sense of the word. So, to think of "right" and "justice" as meaning the same thing in this proper context is absolutely correct.
http://www.paleothea.com/MinorsA-E.html#D