I used to tell my mum that google turns off the internet after 7pm so that I didn't have to help her
Why would you tell her that and not help her?
I'd lie to her face every now and then.
You should generally not lie to someone. It's especially bad to be not telling your parents the truth.
It's fine, she found other ways to get help.
Your mom was asking and depending you for help, you should want to assist her in any way possible. Your mom loves you and values your input, show her that you love her back as well by helping her.