Legal Eligibility for Granting A Loan Act of 2011 - Requires each applicant for a single-family home mortgage to provide the lender information to verify the applicant's citizenship or alien status through the E-Verify program if the home mortgage is to be: (1) newly insured under the Federal Housing Administration (FHA) mortgage insurance program of the Department of Housing and Urban Development (HUD); (2) newly purchased by the Federal National Mortgage Association (Fannie Mae) or the Federal Home Loan Mortgage Corporation (Freddie Mac); or (3) newly made, insured, or guaranteed by the Secretary of Veterans Affairs (VA) or by any other agency or entity of the federal government.