I don't know if the Mundane authorities even knew ... it all happened while the Beast was blocking out the sun, and the offices were rebuilt and repopulated by the next time Angel's crew encountered them as if nothing had ever happened. I imagine they got their reality-rewriting spellcaster to touch things up. =)

Lilah was actually stabbed in the throat, I think, in a manner that would make it look like Angelus had killed her, that brief time they let him free to take down the Beast. When in reality, possessed-Cordelia had done it. Not knowing that, though, Wes cut her head off with an axe so she wouldn't revive as a vampire. IIRC, when they meet her again at the end of Season 4 when she presents them with the offer to take over W&H, she's wearing a scarf, and at one point removes it to demonstrate that her head was just stuck back on, not actually healed.