Interested in Language
Source: Mythology The Gods,Hesiod lived near Helicon, one of the Muses' mountains, the other were Pierus in Pieria, where they were born, Parnassus and, of course, Olympus. One day the Nine appeared to him and they told him, "We know how to speak false things that seem true, but we know, when we will, to utter true things." They were companions of Apollo, the God of Truth, as well as of the Graces. Pindar calls the lyre theirs as well as Apollo's, "the golden lyre to which the step, the dancer's step, listens, owned alike by Apollo and the violet-wreathed Muses." The man they inspired was sacred far beyond any priest.
I know the meanings of each word but I can't understand the blue part as a whole. Would you please be kind enough to clarify the blue part to me? For example, the cases which make me more confused in the blue part are the usage of these words: "theirs" and "owned alike"
Thank you so much