On the same day a judge issued a bench warrant for her arrest, Lindsay Lohan settled her $100 million lawsuit against E-Trade, after it featured a “milkaholic” baby named Lindsay in a Super Bowl ad.

The commercial featured the group of talking babies who play the stock market using E-Trade services. The “Girlfriend” ad ran during the 2010 Super Bowl and featured a male baby apologizing to a female baby for not calling her the night before.

Suspicious, the female baby asked if that “milkaholic Lindsay” was over. Another female baby’s head popped onto the screen and asked, “milk-a-whaaat?”

Lohan filed suit in New York state court, claiming that E-Trade violated her publicity rights, and sought $50 million in compensatory and $50 million in exemplary damages, as well as an injunction. Her lawyer said that Lindsay had single-name recognition, like Oprah or Madonna, and that E-Trade used her celebrity status for its own profit.

A spokesperson for the company that produced the ad said it “just used a popular baby name that happened to be the name of someone on the account team.” E-Trade said in a statement that the suit had no merit, and filed a motion to dismiss the suit in May.

In late September the parties settled the case, with Lohan withdrawing the suit with prejudice. The terms of the settlement are undisclosed.

In a statement, the company said that “E-Trade has always maintained that the claims were without merit, which is why we moved to dismiss the case. With the case now withdrawn, we are pleased to have the matter behind us.” When asked if the settlement included a cash payment, a spokesperson said, “It was a simple business decision. We always have to consider the cost and time involved in litigation, and we are pleased to have the matter behind us.”

Lohan’s lawyer had no comment other than to confirm the settlement, but her mother, Dina, told reporters that the family was “pleased.”

Why it matters: Settling the case allows Lohan to focus on her other legal problems, including a current probation violation for failing multiple drug tests. And had the E-Trade suit gone forward, Lohan faced a tricky legal argument: that the single-name recognition E-Trade allegedly traded on was that of a party girl whom the public knows and understands as someone who imbibes too much “milk.” But the case also demonstrates the expanding notion of publicity rights, where celebrities consider more than just their likeness protectable. Advertisers should be aware that the use of qualities associated with celebrities – positive or negative – could trigger a potential lawsuit.