I searched Google's Ngrams and Google books for "living impaired." There are sporadic hits in the corpus of scanned books for those two words in succession. However, prior to the 1980s, none of these were actually the expression in question. There were few enough hits that I could check them all, and they came from phrases like, "... having their standard of living impaired by...." There was one authentic occurrence of "family-living impaired," but this was not in reference to someone who was dead but rather to an elderly family member with dementia, who was no longer able to live at home with family but had to be placed in a nursing home.
However, the earliest instance of "living impaired" as a jocular way of referring to the dead was not The Simpsons, but in this dialogue from the 1984 novel Murder on Embassy Row: A Capital Crimes Novel, by Margaret Truman:
"... Speaking of morgues, I talked to Jill in forensics today."
"Why do you say that?"
["]Would you want your daughter to spend her life playing with the 'living impaired'?"
Of course, the "living impaired" in this instance are ordinary stiffs, not undead zombies, but the joke is the same.
If there is another earlier instance of the joke, from a source that is not in the Google Books corpus, it cannot be much earlier than the 1984 date for Murder on Embassy Row. The earliest instance of this meaning of the word "impaired" (glossed as "humorous. Lacking or deficient in the attribute or field specified. Used in contexts not usually requiring careful use of language in order to avoid giving offence, but humorously regarded as doing so") in the Oxford English Dictionary is from November 1982: "We serve television for the humor impaired," from the Washington Post. (Bart's quote from the "Treehouse of Horror" episode is also listed in the OED entry.)
Truman's book was not a bestseller, so the writers of The Simpsons probably came up with the joke independently.