The question *does* include the word "federal." It is not whether someone gave you a free lunch; it's whether or not anyone in the household received federal free/ reduced price lunch during the two year look-back.
Here is the paper FAFSA. The question is after question 73 and applies to questions 74-78. http://www.fafsa.ed.gov/fotw1213/pdf/PdfFafsa12-13.pdf
In 2010 or 2011, did you, your parents or anyone in your parents’ household (from question 72) receive benefits from any of the federal programs listed?
74. Supplemental Security Income (SSI)
75. Food Stamps
76. Free or Reduced Price Lunch
77. Temporary Assistance for Needy Families (TANF)
78. Special Supplemental Nutrition Program for Women, Infants and Children (WIC)