I am going to assert my personal knowledge here.
I actually saw 'Star Wars' in 1977, several times, on its original release. In the original theatrical version there is only a single shot.
Bear in mind that they are sitting down, at a table in the Cantina bar, opposite each other. Greedo goes for his gun, saying, "I'm going to enjoy this". There is a muffled blast, and a flash, as Solo, in self defence, fires under the table, without even drawing his blaster from its holster. Greedo slumps face-down on the table, dead.
I don't understand where the suggestion has come from that Solo shot him in cold blood. Greedo quite plainly grabs for his own blaster, and even has time to deliver his gloating line; his intention to murder Solo is perfectly clear.
Solo merely waits, to see what Greedo's intention is. It is only when that intention is clearly demonstrated, and Greedo is actually in the act of going for his gun, that Solo fires.
That shot got a big laugh, because Greedo was so clearly not expecting it, and so obviously thought Solo was entirely at his mercy. But, unexpectedly, Solo shoots him - without even drawing his weapon. His innocuous, unthreatening posture took the audience, and Greedo, completely by surprise; and the unexpected reversal - with Greedo shot dead instead of doing the shooting - got a well deserved belly laugh.
Lucas is mistaken. The reason why audiences reacted badly to his later tampering with this scene was because they wanted to preserve that laugh.
The whole point of the scene is to introduce the character of Han Solo with a joke and a belly laugh. Greedo thinks he's got the upper hand; but Solo demonstrates how clever and resourceful he actually is, behind his harmless pose. It's an Indiana Jones moment, pulling his chestnuts out of the fire unexpectedly, and at the last possible moment.
Audiences wanted to associate Han Solo with that particular laugh, because that's how he was first introduced to them in the entire 'Star Wars' saga. They resented Lucas for later tampering with a scene that was already perfect, and that perfectly summed-up the character.