It sounds like a phase where it's more about exerting her own independence and control, rather than a sign that she's going to be lying continously from here on.
She's 10, she does need parental guidance, but it's so different from now on... your job as parent is changing and you have to re-think the strategies. Whether or not she ate breakfast is really not important.... she's probably not starving... so don't ask. The same with brushing her teeth. Yes, it's gross, and you do pay the dental bills, but a cavity is a really good learning experience.
Yes, lying is a very big deal. So don't ask questions over simple things with "yes/no" responses. Open conversations up where she can choose a little control.
Try asking "what do you think about breakfast?" As a mother of 3 teens, I know the answer from my darling trio might be, "you are soooo weird, why do ask those things?" or "I think it's stupid." or "uhm, yeah, where is it?" At least, it engages them and they can't just brush off the answer, which is likely what your daughter is doing. She wants some independence and control and she sees your questions as bothersome.
Talk to her about things she's interested in, give her the chance to talk to you and tell you things and at least she'll have less opportunity or motivation to lie.
Good luck!