It's not about the soap. It about not being honest. We do use other soap in her washroom. She's been asked not to use our washroom as the marble countertop is pourous. I actually don't care about the soap at all and I've told her as much. I care that she won't answer simple yes or no questions lately. This issue extends into other areas of her life right now.
One thing that helped when my kids were going through that phase was to simply stop asking them questions.
For example, the soap. You already know she's the one who used it in the sink. So, rather than asking, "Did you use the soap in the sink?" you simply say, "Ah, you used the soap in the sink," and then state the consequence. If she then tries to deny it, you give her the old gimlet eye and refuse to acknowledge her ridiculous attempt at putting one over on you. If necessary, send her to her room and tell her she's welcome to come back when she's ready to apologize for insulting your intelligence.
My husband used to terrify the kids, just by asking, "Do you
really think I'm that stupid?"
Cut down on her opportunities to lie, and she'll do it a lot less. Convince her that she's a terrible liar and that you can tell right away, every time she tries to lie to you.
When you ask her a direct question, you're virtually asking her to lie to you. Setting her up to lie and then trying to force her to admit she's lied, will only create power battles, and that's no fun for anyone.
And when you tell her that "the punishment is worse if you lie to me," you're just making it worse.
From her perspective... If she tells the truth, she's in trouble for sure. If she lies, and you believe her, there's no punishment at all. So she's choosing between a guaranteed (if somewhat smaller punishment) or no punishment at all. Every time she lies, she's rolling the dice on a chance that she might get away scott free. Kids are naturally optimistic about that kind of thing, and like any gambler she's going to keep trying for the jackpot "no punishment" over "smaller punishment". So don't ask.
If it helps, the fact that she's trying to lie to you is actually a great sign, developmentally speaking. It means she understands that you have a different perspective of the world, and she's trying to manipulate it to her benefit. Lying and empathy develop hand in hand. Kids who can't lie, frequently can't understand another person's point of view, either. It's not a fun phase, but it's a necessary one.