Lilly's mom was tested positive for Feline Immunodeficiency Virus.  So Lilly and her siblings were tested positive also.  
But upon much research our vet tech found very useful information from Cornell University.
"Because few, if any, cats ever eliminate infection, the presence of anitbodies indicates that a cat is infected with FIV.  This test can be performed by most veterinary diagnostic laboratories and also is availabale in kit form for use in veterinary clinics.  Since FALSE-POSITIVE results may occur, veterinarians recommend that positive results be confirmed using a test with a different format.  Infected mother cats transfer FIV antibodies to nursing kittens, so kittens born to infected mothers may receive a positive test results for several months after birth.     HOWEVER, FEW OF THESE KITTENS ACTUALLY ARE OR WILL BECOME IN FECTED.  To clarify their infection status, kittens younger than 6 months of age that test positive for FIV should be RETESTED at 60-day intervals until they are at least 6 months old.