No, but "last Sunday" is correct.
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I believe that rather than saying "last Sunday" in the latter instance, you would possibly state the date or say "this past Sunday". The aforementioned would be easier and more relevant if it was, in fact, more than a week.
"However, suppose it is Wed., May 16, and you say, "I went to a party last Sunday.", the meaning is not so clear. Do you mean the party was on Sun., May 13, or on Sun., May 6? Further information would be needed in order to be completely clear.
I've never encountered a native speaker who in this example would think last Sunday meant May 6."
I'm a native English spe