Having personally talked to an attorney about spreading truth about abuse of animals, and in our case their wasn't even any arrests, IMO it is absolutely safe to speak the truth about it. You can absolutely tell her employers that she was arrested for animal cruelty because she reacted out in a violent anger towards an animal. That is truth. Not slander. Now, I still would personally tell her face to face, or over the phone. Writing almost always is a bad idea.. but all those people that threaten to sue for slander... well, its mostly a joke. A slander case is VERY hard one to make.
So please, do inform her! I'd be careful treading on ground in which they are friends, and wouldn't detail the attack this person made against Lilly, but saying just little info I said above^^ would in no way be slanderous.