I thank you Kassios for those good links. You are right that "LAODIKOS" means "tried by the people". I see no reason however why "LAODIKE" (Laodice) must mean LAODIKOS. As you point out, the meaning of the Ancient Greek name "LAODIKE" is obviously obscure.
Have you noticed that EURYDICE (Eurydike) is a combination of ευρυς (eurys) "wide" and δικη (dike) "justice"?
http://www.behindthename.com/php/view.php?name=eurydice
I am aware that Ancient Greece came before the Seleucid dynasty. It's just not obvious to me that the name LAODIKE ever meant anything in ancient history. Isn't it possible that the modern explanation of LAODIKE meaning LAOS + DIKE is just a pun?