Was there ever an explanation given by George Lucas or the studios for changing the cantina scene to Greedo firing before Han did?
Yes, Lucas addressed this controversy in an interview with The Hollywood Reporter in 2012:
Lucas: The controversy over who shot first, Greedo or Han Solo, in Episode IV, what I did was try to clean up the confusion, but obviously it upset people because they wanted Solo [who seemed to be the one who shot first in the original] to be a cold-blooded killer1, but he actually isn't. It had been done in all close-ups and it was confusing about who did what to whom. I put a little wider shot in there that made it clear that Greedo is the one who shot first, but everyone wanted to think that Han shot first, because they wanted to think that he actually just gunned him down.
He goes on to compare this change to replacing the puppet Yoda in Phantom Menace with the CGI model used in Attack of the Clones and Revenge of the Sith. Ultimately, this is an example of Lucas using CGI to make older films more true to his creative vision; in Lucas' mind, Greedo always shot first.
Interesting, this is contradicted by the script:
Greedo I've been looking forward to killing you for a long time.
Han: I bet you have.
Suddenly the slimy alien disappears in a blinding flash of light. Han pulls his smoking gun from beneath the table as the other patron look on in bemused amazement. Han gets up and starts out of the cantina, flipping the bartender some coins as he leaves.
The novelization (which, despite having Lucas' name on the cover, was actually written by Alan Dean Foster and presumably approved by Lucas) also contradicts Lucas' statement:
"Over my dead body," Solo said unamiably.
[Greedo] was not impressed. "If you insist. Will you come outside with me, or must I finish it here?"
"I don't think they'd like another killing in here," Solo pointed out.
Something which might have been a laugh came from the creature's translator. "They'd hardly notice. Get up, Solo. I've been looking forward to this for a long time. You've embarrassed me in front of Jabba for the last time."
"I think you're right."
Light and noise filled the little corner of the cantina, and when it had faded, all that remained of the unctuous alien was a smoking, slimy spot on the stone floor.
Solo brought his hand to the smoking weapon it held out from beneath the table, drawing bemused stares from several of the cantina's patrons and clucking sounds from its more knowledgeable ones. They had known the creature had committed its fatal mistake in allowing Solo the chance to get his hands under cover.
Star Wars (novelization) Chapter 7
No mention is made of Greedo shooting at all. Chalk it up to Lucas' historical revisionism, I guess.
However, they've been slowly rectifying this with subsequent releases:
The initial controversy came from the 1997 Special Edition release
In the 2004 DVD release, the timing is shortened slightly; Greedo fires first, but only just. A diligent YouTuber has compared the 2004 scene to the 1977
1 I understand that this is a topic that incites passion. Please keep the discussion in comments respectful to all2, especially those with different opinions. We're all friends here, let's keep it that way.
2 Except for George Lucas, for whom Nerd Rage has been justified (even mandatory) since 1997