You are correct that the meaning of 'the camera loves me" means that the person in question photographs well and looks good on screen. And yes, 'the' is necessary. "Camera loves me' is not a proper sentence.

A camera cannot actually 'love' someone, so this contradiction gives the expression a sense of fun.

You are correct. There is an adjective that describes a person that looks good in pictures. The adjective is : Photogenic. Definition of photogenic in English: adjective 1. (Especially of a person) looking attractive in photographs or on film. 2. Biology (Of an organism or tissue) producing or emitting light. "We were very photogenic, apparently, as we seemed to attract many people with cameras as we congregated in one spot."

"The camera loves me", is 'the' needed? You are correct that the meaning of 'the camera loves me" means that the person in question photographs well and looks good on screen. And yes, 'the' is necessary. "Camera loves me' is not a proper sentence.