Weak and ineffectual person (7)
(Other definitions for doormat that I've seen before include "Item for wiping shoes on" , "Submissive person (colloq.)" , "Shoe wiper at entrance" , "wimp" , "On which shoes should be wiped" .)
(Other definitions for lame duck that I've seen before include "Unsuccessful person" , "Useless person or thing" , "Inefficient or helpless person" , "Ineffectual type" , "Feeble person" .)