Lucario is based on the Anubis, witch is based on a Jackal, witch last I checked wasn't blue. So does Lucario being blue have anything to do with his aura gimmick or is it just a color the designers liked? Same goes with his shiny being yellow.
Yes, it most likely does. Aura is normally depicted as a blue field of energy surrounding an object, signaling its emotion and/or thoughts. Since aura is normally depicted as shades of blue and a secondary color of gold/yellow, the designers might have colored him that way to go along with his "aura".
But only the designers of Pokemon know for sure.
No, I don't think so. It's just a color the designers liked. Aura Sphere is blue, but Aura does not actually exist, so there isn't anything to bas it on. Besides, why would the Shiny be gold, then? That's got nothing to do with Aura. I think Aura Sphere's color was based off Lucario rather than the other way round.