Lady Gaga’s big-screen debut in Robert Rodriguez’s “Machete Kills” came thanks to a chance encounter in an LA tattoo parlor. The film’s star,Danny Trejo, was getting some new ink at Shamrock Social Club in LA, right next to Gaga, shortly before the movie started production, a spy said. When the “Poker Face” singer overheard Trejo saying his next project would be a “Machete” sequel, Gaga piped up and said she’d like to work with Rodriguez. “Danny called Robert and told him Gaga wanted to be in the movie,” our source said. By the time Trejo showed up on the set, Gaga was in the film that had also castSofia Vergara, Charlie Sheen, Mel Gibson, Jessica Alba, Antonio Banderas and Vanessa Hudgens.