Does the right to privacy established in Lawrence vs. Texas protect the right of the defendant to engage in sex work?

 For my sex and the law class i have to create arguments for an appellate brief of a case my group and i created. Our fact scenario is The defendant is a transgender woman who is charged by an undercover cop for soliciting sex. The defendant is looking to dismiss the charges on the grounds of trans phobic entrapment.Our issue statement is: Does the right to privacy established in Lawrence vs. Texas protect the right of the defendant to engage in sex work? I am on the defendants side, so I have to come up with 3-4 arguments to argue why the defendant should not be charged and why sex work should not be illegal/punishable. If you can please just create arguments that are backed up with facts and cases that would be wonderful and alot of help. Thank you so much!