Under Title III, no individual may be discriminated against on the basis of disability with regards to the full and equal enjoyment of the goods, services, facilities, or accommodations of any place of public accommodation by any person who owns, leases, or operates a place of public accommodation. Public accommodations include most places of lodging (such as inns and hotels), recreation, transportation, education, and dining, along with stores, care providers, and places of public displays.

If you do get sued, if you immediately remediate your website, you may be able to get the lawsuit dismissed on mootness (there’s no longer anything in dispute, i.e. plaintiffs are arguing your website is inaccessible but you’ve already made it accessible). This definitely does not mean you should wait to fix your website but it does mean you may have an out.
The Americans with Disabilities Act of 1990 (ADA) makes it unlawful to discriminate in employment against a qualified individual with a disability. The ADA also outlaws discrimination against individuals with disabilities in State and local government services, public accommodations, transportation and telecommunications. This booklet explains the part of the ADA that prohibits job discrimination. This part of the law is enforced by the U.S. Equal Employment Opportunity Commission and State and local civil rights enforcement agencies that work with the Commission.
The Department has assembled an official online version of the 2010 Standards to bring together the information in one easy-to-access location.  It provides the scoping and technical requirements for new construction and alterations resulting from the adoption of revised 2010 Standards in the final rules for Title II (28 CFR part 35) and Title III (28 CFR part 36).
Courts have taken essentially the following position on the issue of whether websites are places of public accommodation: Website accessibility fulfills the spirit of the ADA by lowering the barriers for people with disabilities to participate in business and commerce. As such, commercial websites need to comply with ADA regulations. Judges have reached this conclusion in several high-profile cases, such as the National Federation of the Blind’s lawsuit against the Scribd digital library. As a result of this case, Scribd agreed to redesign its website to work with screen reader software by the end of 2017.
Talk to your web designer about other techniques that will make your site more user-friendly for people with disabilities. Worried that’s not in your budget? Consider the fact that DOJ fines start at $75,000. And it's still yet to be determined if a non-compliant website is liable for one fine or will be charge per page for each violation. As the recent lawsuits illustrate, though, settlements quickly add up into the millions.