How do I explain to her that she shouldn�t tell me she wants to nurse, go potty etc. if that is really not the case??
That's not lying - it's engaging in the behavior that gets the desired result.
Stop reinforcing "If I ask for what I really want, I won't get it. But if I ask for something I don't want, I get what I do want."
The PP's suggestion (give her the undesired thing she asks for she asks for, but not what she wants) is one alternative. You might also try giving her the desired thing when she asks for it for a while (to reinforce the behavior you want), or explaining your reasoning to her (although IME this invites negotiation, which I personally don't mind, but which you might).
We had nothing to play with in the bedroom or bathroom at that age, so the most interesting place to play was the living room. And my DD was physically cautious, so could be left mostly-unsupervised without calamity while I did stuff I needed to do. She might be covered in washable marker, but wouldn't be perched on top of the refrigerator.
