If that was Lucas's intention, he did a pretty bad job of communicating it. The scene makes it clear that Greedo intends to take Han back to Jabba, who will kill Han, then take his ship.

Greedo: You can tell that to Jabba. He may only take your ship.
Han: Over my dead body.
Greedo: That's the idea.

Greedo refers to bounty hunters, not hitmen, pursuing Solo; most secondary sources suggest that Greedo is a bounty hunter as well. Return of the Jedi reinforces the idea that Jabba employs bounty hunters to bring him his enemies alive ... he enjoys making artwork out of them, feeding them to his pets, etc. Han has a deathmark on his head, but the O-OT shows us that he was to be delivered alive to Jabba.

Lucas's original intention may have been otherwise, but what he realized is superior in terms of character arc and believability. He diminished both when he failed to recognize the results of a happy accident (or his editors).