Blended and step families are tough. It's important to figure out why your daughter lied to her stepfather but told her the truth. I'm not sure of all the details, but here are some basic principles to follow while parenting in a blended family:
-Parent as a couple, so the kids see you as a united front.
-Argue in private
-Treat all kids the same- biological and step kids
-Create a set of house rules or guidelines for all the kids who live or visit your house- and have consequences based on their developmental stages
I hope that helps. There is a reason your daughter didn't share that information with her stepdad. You may want to ask her, and then - after you listen- talk through it with her.
I wish you the very best.
Shirley Cress Dudley, MA LPC NCC FACMPE
Blended family, stepfamily and single parent expert
Director of The Blended and Step Family Resource Center
Author of Blended Family Advice