She also gave the Lone Star State some credit, adding, "Texas turns it out."

"Making this movie was already the gift, every element of it. To share it with you all and feel the love returned to us was the best feeling. Thank you for having us Austin," Lively added.

Lively and her It Ends With Us director-costar Baldoni, 41, are currently in the middle of a highly publicized legal battle. In December, Lively sued Baldoni, accusing him and others of sexual harassment and a retaliatory smear campaign, which he denies. Baldoni countersued Lively, her husband Ryan Reynolds and their publicist in January, alleging defamation and extortion.

The SXSW premiere for Another Simple Favor was Lively's first big movie event amid the legal drama. However, the Age of Adaline actress and Reynolds, 48, did attend Saturday Night Live's 50th anniversary special in February. Their situation was mocked on SNL during the March 1 episode after Reynolds briefly referenced it during SNL50.

"Blake felt a bit anxious about attending the SNL anniversary. She still thought it was the perfect opportunity to ease back into the spotlight," a source told PEOPLE after SNL50 aired. "They had many friends attending, and as soon as they arrived, they received a warm welcome. It was a great event."

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"Blake wouldn't mind staying out of the spotlight for longer, but she has to get back to work with Anna Kendrick soon anyway," the insider added, referring to the Another Simple Favor promotional tour. "She feels more ready now. She knows it will be a long year with continued drama, but she's just trying to focus on the good things. Her family is everything to her."