The singer has offered the cash for their return with “no questions asked”.
Ryan Fischer, 30, was walking French bulldogs Koji, Miss Asia and Gustavo in West Hollywood on Wednesday night when he was targeted outside his home.
Last night he was in a “serious condition” in hospital, though doctors insisted he was recovering well from the attack.
Lady Gaga yesterday set up an email account for the stolen dogs – Koji and Gustavo – asking anyone with information to get in touch.
Police said it was too early to know if the attack was a robbery by opportunists, or related to local gangs.
Video at the scene showed a man on the ground still clinging to one dog, Miss Asia.
Mr Fischer appeared to be alert and talking after the shooting, although struggling to breathe.
Later, home surveillance emerged capturing the moment he was shot.
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