Before I get into the answer, I think you're better off saying "do as I tell you" and not "do as I told you" because you're using present tense for the others. Not required, but it's more appropriate. Otherwise, it sounds as though you are receiving resistance from the person already (the "telling" was past, but the "don't say" or "don't give" is present, meaning it's probably happening. If you're just saying a general sentence, then all present is best.
Now for your meaning problems: "Lips." No one will ever say it in the plural form. To "give lip" is sufficient because "lip" is an uncountable collective (if I'm not mistaken) in meaning (can be "she gave me a lot of lip over it"). But never say it with the plural of "lips," or else it really sounds like you cut your lips off and gave them to someone else (or received someone else's lips).
Other than that, it seems fine. One thing to keep in mind is you repeating the same thing. "Natural" speech would omit the last part, so that the sentence would be (with corrections from above): Just do as I tell you, and don't give me any of your lip. I won't be having it. (You can also just say "I won't have it," or "I won't have it with you," which I think is more natural)
For the last sentence, the only major problem is "I won't be having none of it." If you say that, it means you WILL be having it. "None" is nothing, and if you want nothing, that means you want something. just do as I tell you and say nothing back. I won't have any of it. (Same note as above for why I would leave the progress out unless you're trying to emphasize the meaning in some special way.)