1. A is lying to B, and they know that B doesn't know the truth. The intent is to make them believe the lie, which is intentionally misleading them and bad faith
2. A is lying to B, and they aren't sure if B knows it's a lie. The intent is to make them believe the lie, which is intentionally misleading them and bad faith
3. A is lying to B, and they know for sure B knows it's a lie. The intent is either to provoke an emotional reaction from either B or someone observing (which is bad faith), or performative for others who will see the lie and might fall into categories 1 or 2, which is bad faith
I don't understand how anyone could plausibly argue that lying to someone intentionally isn't bad faith. Maybe I'm the one falling for category three here