It can be difficult to provide a clear answer without spending a lot of time getting to know you and your family. The best way to stop lying in my house will not be the same as yours. However, from your word choices, I can see what looks like a path forward. Feel free to have your own opinion on it.
The key phrasing for me was "My daughter knows we value honesty above everything in our house." Now from a philosophical perspective, one can argue that we never know what someone else is thinking. You assert that your daughter knows you value honesty, and its totally valid to make that assertion. You may even be right. However, it is in conflict with the evidence. She's acting in a way which challenges that assumption. This, to me, points in a direction to start digging.
It's entirely possible that, in your house, you'd really rather her murder someone than lie about something. Who am I to judge? Far more likely than that extreme outcome is that you actually have a rather complicated set of values in your house. I don't know a household today that doesn't have a complicated set of values, so this wouldn't be all that unusual. In such a situation, your daughter may not be interpreting your priorities in values the same way you think she is. The easiest way for two people to fail to communicate is to start from faulty assumptions. It's best to make sure you give enough time to clarify these along the way.
Of course, this is also the kind of topic that is really hard to talk about. What you need is time. You need to give time for you and her to communicate on this topic.
This incident has shook the confidence I had in her.
I think your opportunity lies here. Step 1 will be repairing your confidence in her. Easier said than done, right? In theory, she should be the one who has to act to repair your confidence right? Well, that is the normal course of things, but you're a parent. You get stuck doing things because your kid doesn't. That's the name of the game.
Consider trying to adjust your own mind such that, instead of having your confidence shaken, you still have your confidence in her, but it is under attack. Something (i.e. this event) is in the process of shaking your confidence. This shift can be hard, but it opens a door for her. Damage that is done is done, but damage that is in the process of being done can be responded to. Give her something worth responding to. Show her how this event is destabilizing your confidence. Let her feel what it will do to your relationship -- not in one big slug, but slowly in a steady way which lets her feel just how bad it is. She doesn't need to comprehend the depth of the hole she needs to get out of, but she does need to be able to feel how steep the walls are, and how far the edge is away.
Finally, be flexible about the outcome. You and I both know you don't want your confidence in her shaken. You want this thing to be resolved. Be flexible. I mentioned earlier the assertion "My daughter knows we value honesty above everything in our house." Maybe your confidence can get a boost from you better understanding what your daughter really knows. Maybe you don't get to the point where you feel she will always be perfectly honest, but you gain some other unifying factor which neither of you even thought to look for until you started looking. People are complicated, and if we had all the answers when we started, where would the fun be?
I can't say its a full solution for a lying daughter, but the path has some merits. Most of the things that need to be done at first are done by you, to you. You start out on a path that's independent of her, and only as you communicate does the work shift more and more towards her. This gives you control over your life, and I have a feeling that's a big thing for you right now!
My prediction would be that, if your daughter can see that she can't disturb your inner calm with her life choices, but does have to answer for them when the bell tolls, you and her will come to an agreeable solution.