I'm going to ignore my mom because she lied to me.
That's a shocker. What did your mom lie to you about?
She lied to me about why she had to leave dinner when it was just because she was on her period.
She shouldn't have lied to you but she probably did because she was embarrased. That being said you shouldn't just ignore because of something small like that if at all. They love and took care of you so don't hold a small thing like that over their heads.
I will do it, she deserves it. I'm doing this because she lied to me.
I understand you are hurt because she lied to you, and I believe you should confront her about it rather than ignoring her. She might feel even worse if you cut her off for something so small. It's better to get her perspective on things as well.