I skipped all the posts for fear of spoilers.....all I can say is: I am loving the hell out of this show so far. I am only halfway through season one on Netflix. James Spader rocks, and Megan Boone is a hotttaaaayyyyyyyyyyy!!!!!
Lizzie being Red's daughter is too obvious, so being a network TV show they could easily go there. Although you would think the FBI would've already performed a DNA test as soon as Red requests to work with some nobody agent who happens to be adopted and doesn't know who her biological father is. It's possible Red is looking after her as a debt to her biological father who he either killed or failed to save. Or she's the daughter of whoever is No. 1 on his blacklist.
I think that she's a substitute for his own dead daughter. No biological connection whatsoever (that would be painfully obvious). She represents the innocent life that he lost and can never have again.