Gaga, whose recent performances included singing the national anthem at President Joe Biden's inauguration last month, has been in Rome filming a movie. Her three French bulldogs remained in Hollywood, The Daily Mail reported.
The outlet said Gaga's dog walker was walking the dogs on Wednesday evening when he was shot. The third dog, Miss Asia, escaped and was later recovered.
Shortly before 10pm on Wednesday, a male gunman wielding a semi-automatic handgun shot a male in his 30s in Hollywood and fled in a white vehicle, stealing two French bulldogs, Los Angeles Police Officer Drake Madison said.
Fire department paramedics took the male victim to a local hospital where he was in critical condition from a single gunshot wound, police said on Thursday.
The source close to Lady Gaga, who spoke on condition of anonymity, said the singer was urging anyone who has the dogs to contact them via email to return the dogs and retrieve the reward, no questions asked.
The French bulldog is a popular breed, and there has been a growing trend of the dogs, which can cost several thousand dollars as puppies, being stolen for resale or breeding.