I can't justify telling the child "your other parent is lying".
Why not? Eventually your child is going to find out that their dad is lying and then ask you if you knew? Your child has to be able to trust one of you. I was honest with all our children from an early age. They knew things weren't right and they appreciated knowing what was going on with their alcoholic dad and my concerns for their welfare when with him.
I agree with Redatlanta. Even if nothing happens why subject your child to a situation you yourself have got out of? You cannot know what is going on and what dangers your child maybe placed in.