I dont agree with the spanking but however there was a consequence for the action that both children were aware of. If you choose not to follow this through then the consequences of that decision will be that the children will learn that they can get away with things. Good luck with your situation.
Yes, she lied to you both about something very serious. That is precisely the type of behavior when my husband and I spank our kids. Make sure your husband does it though. I've learned that works better. I have a hard time doing it and I know my oldest would prefer it if I do it.