I'm currently in the position of either having to either tell a small lie or tell the truth, which would be a bit hurtful, embarrassing and cause a bit of bad feeling 
Usually, in this type of situation, I would just make a random excuse, but I'm being received into the Catholic Church in a couple of weeks and want to be faithful and not tell lies.
I'm currently avoiding the person, but I'll run into her eventually, as it's another parent at school.