What did you want Lulu to do? The fact is, the geass went out of control at the worse possible moment. He was unable to physically stop her from committing the act. Therefore, the only thing left for him to do was to kill her in order to end the geass.
And for the propaganda? Inevitable. There was nothing else he could do there as well. He couldn't just walk away from the event and pretend it never happened. No, he had to take the chance and use it to his advantage.
That's his greatest strength and weakness. He will always, always think about the best possible efficiency.
And you know, he regretted it. He cried and felt remorse over everything. He didn't kill Euphemia and enjoy it and than laugh in private. No. He cried in C.C.'s arms over the catastrophe he created.