Q. If my citation has an organization as the author, what do I put in the parenthesis for the in-text citation (for MLA style)?

You would still place the organization in the in-text citation. According to MLA you can use abbreviations such as "Assoc." for association or "FDN" for foundation if that is part of the organization's name. Here's an example:

Citation as it appears on the Reference List:

American Lung Association. "Smoking Facts." American Lung Association. 2017. http://www.lung.org/stop-

            smoking/smoking-facts/. 

Corresponding in-text citation

As many as 480,000 people die annually in the U.S. from tobacco use and second hand smoke in spite of the regulations placed on the tobacco industry and sale of cigarettes (American Lung Assoc.).