As far as I know, "Ajax" is not a word but a proper name. I was not able to locate it in the long first act in my edition of King Lear without a line number. Ajax was a formidable Greek warrior, second only to Achilles in prowess. He figures prominently in Homer's Iliad. He has a tremendous man-to-man battle with the Trojan hero Hector with both the Greek and Trojan armies watching. Although Ajax is physically very powerful, he is depicted as not exceptionally intelligent. He is also included as a character in Virgil's Aeneid and in Shakespeare's Troilus and Cressida.