In (American?) English "lap-dog" used literally means a canine of such small size and placid demeanor it will happily stay in your lap for expended periods.
Applied to a person, it is a perjorative meaning someone so ineffectual or submissive they are easily controlled to their own detriment. (Usually by a single person.)
I am looking for a colloquial expression or well-known literary reference in Chinese (either Mandarin or Cantonese is fine.) that carries the same meaning. Preserving an animal reference would be even better.