no it wasnt about DID. she did some interviews. her songs reflect her being gay and being abused because of it. in an interview about sum of parts she said the titile and words sum of parts refers to the physical body, skin, arms legs, physical looks and that looks are only skin deep, she also said during the interview that the song was about her being bullied/abused because of being gay and surviving a rape dduring her adult life that left her with scars. and that message if anything is that regardless of the being bullied about being gay, regardless of being abused and scarred to love your body, just be yourself, not to limit yourself according to what others want you to be.

if you type in the search bar the words mary lambert interviews you will find many articles and interviews she has done about each of her songs.