You can do it either way. If you go to NYU s Drama Department in the Tisch School of the Arts you can attend Lee Strassberg as part of your NYU studies. But you can also attend as a private student.I attended the Strassberg Institute decades ago as part of the NYU program. But there were always private students around the studio as well. However, the NYU students are in separate classes.
http://www.strasberg.com/ Go to admissions. It makes no mention of NYU.