I think that is the main reason that the FBI checked out Lee for paternity. Casey lied about who the father was, giving out two names of DEAD guys. So the FBI would obviously think she was hiding something. Oh, and the name 'Caylee' being a hybrid of Casey/Lee is kind of odd and creepy.
Maybe either the father totally dissed her and wanted nothing to do with her and that's why she doesn't want him to be known, because she doesn't want him to tell why he didn't want her? Or perhaps a teacher from school she'd been having an affair with? It could have lasted after high school? Just hypothesizing. I'd really like to know, even though it doesn't matter much to the case. IMO.