Twilight star Lautner was recently rumoured to have begun dating 21-year-old Lily, whom he met on the set of upcoming film Abduction.
According to Star magazine, Lily recently arranged for her new boyfriend to meet her rock star father, who was apparently won over by Lautner.
A source said: "[Phil's] pretty tough on the guys Lily introduces him to. Taylor was nervous about meeting him, but they got along well."
Earlier this month, Nickelodeon star Victoria Justice denied claims that she was going out with longtime friend Lautner.