There is an inner plastic escutcheon/mechanism on the inner side of the outer handle which has an inner lever with a spring which is bad for seizing causing the play/wear you are noticing,you have to remove the door card for access to the inner lock etc for removal to get at the mechanism,either that or get oil/lubricant onto the spring/pin/lever and work it back and forth to free off,good luck.
cdc
April 2015