It is your choice on what to do, and remember that what ever you do you are doing it for her, not yourself.
Please also remember that you are the best person on weather your dog Lady is suffering , you know her inside and out. If you feel that she is comfortable and not suffering then why choose to put her to sleep. If you think that she is suffering and she is unconfortable then she is trying to tell you that it her time to go - only you can make this desion and do not be forced into doing something that yo have to live with but please bear Lady in mind when making this desion.
I feel that you need more information regarding possible treatments and the stage of cushings that Lady is at.
Please talk you your veterinary surgeon again , you do not even have to take Lady when you return to the vets, please express your views and then hopefully you be able to make a more certative descion.
Good luck hope i have helped xx