He just kid of sits there when he gets the news. Then he starts shaking. Whoever tells him thinks he is crying, and is about to say something when Lelouch suddenly starts laughing on and on. It doesn't stop, it lasts for several minutes. Several minutes of disturbed, cooked laughter.
He abruptly stops, looks the messenger in the eye and tells him "I once wished to make the world better for her. But now she is gone, and that leaves me with one option."
"W-w-what my lord?"
An evil grin crosses Lelouch's face, "To burn it down."