The entrapment is in the INDUCEMENT of a criminal act. Inducement being an deliberately executed intentional action by a law enforcement officer. Specific individual actions (lying about being a sex worker, up to directly propositioning a mark with an offer, and any other related behavior) would be examined and taken as a whole within the context of the situation to determine if the sum of the parts equates to unlawful inducement/entrapment.
It is perfectly lawful for a police officer to verbally lie about being a sex worker, and also by the letter of the law perfectly lawful for a police officer (or any person) to proposition/offer sexual services for consideration to a mark. However, either/or, done together by a police officer, with demonstrable intent beyond a reasonable doubt to induce criminality being the motive for so doing, constitutes an act of entrapment, which is unlawful (to such extent that charges arising from said action will be dismissed.)