If my employer said he gave me official lieu of notice of employment but can''t tell me when my last day is since they outsourced do I have to wait

It is not possible to answer your question in the manner you have phrased it. As a general matter, an "outsourced" employee has a "real" employer and a "technical" employer, and the former determines how long employment lasts. The employee may, of course, quit at any time.