The only obvious connection would be the use of the name "Lindsay," which is not exactly the unique identifier one finds in a name like "Cher." The public does not have unequivocal association between the name "Lindsay" and the person Lohan.
The website rightofpublicity gives background on past, relevant lawsuits, including Zacchini v. Scripps-Howard Broadcasting.
In passing, there is a classic law review article by Warren and Brandeis titled The Right to Privacy Even though published in the year 1890, it mentions "business methods" in paragraph 3: Recent inventions and business methods call attention to the next step...
How much is the use of "Lindsay" worth? :
According to Stephanie Ovadia, the attorney acting for Ms Lohan, her client has the same single-name recognition as Oprah or Madonna: "Many celebrities are known by one name only, and E-Trade is using that knowledge to profit".
Separately, domain name jurisprudence by Gerald M. Levine