Next proper step to answer email - Found out there IS something going on in my research lab - Grad LIED to me?

You should not just deal directly with the professor as the grad asst doesn't seem to have your best interests in mind. I don't think it is good to fight directly with them. I would explain to the professor that there has been come miscommunication (don't directly label it lying as this will not help when you still have to work with the grad asst). Confirm with the professor what potential projects you can work on. Ideally you would then use this email to forward to the grad asst and apologize that perhaps there was miscommunication but you would be interested in working on x,y,z depending on the options which the professor laid out. It seems the grad asst is in the wrong but I think he/she knows it. So if you come up with concrete examples of things you can work on and it shows you have communicated with the professor, there is little the grad asst can say. I think it would not be prudent to accuse the grad asst of lying to the professor or directly to the grad asst because you will have to work with this person no matter what. You need to think long-term.