I am not an American. . . I wonder if being a NYC Bar member is enough to lawfully practice law in NYC or there is a need to have a visa or citizenship.
No, it's not enough. All non-US citizens must have a work visa or green card to take up "gainful employment" in the US. The Visa Waiver Program does allow citizens of specific countries to travel to the United States for tourism or business for up to 90 days, however, it generally applies only to short-term meetings and conferences in relation to the alien's profession/line of business/employer in their home country, not to most forms of "gainful employment".
If you aren't eligible for the Visa Waiver Program (i.e., you intend to be gainfully employed in the US), you will need an H-1B visa, which requires sponsorship by the company/firm you plan to work for.
Good luck finding legal employment in the US in this economy, and good luck finding a legal employer willing to go through the hassle of sponsoring you.