I know I'm way late on this show, but I finally watched the last several episodes. As Kreugen said, Berlin's daughter was clearly the picture from the Stewmaker's collection, so we know Lizzie isn't his daughter. It is questionable whether or not Red would have fucked around with any DNA results to hide him being the father, BUT he has made a point of telling her that he has never lied to her, and he straight up told her that he isn't her father. Sure, he could be speaking metaphorically, but I don't think he'd break his streak. If he wanted to, he'd have lied about killing her step-father and made things a ton easier for himself. But he's taking the hard road and never lying to her, and I think we have to take him at his word on that.
Given the fact that he hasn't ever lied to her, my theory is that Berlin's daughter had a daughter herself, which is Lizzie. Nothing new there, plenty of people have suggested it already. But I think Lizzie's father is NOT Reddington...it is some unknown Really Bad Man that made enemies, the likes of which would hire the Stewmaker and perhaps some of these other Blacklisters to take him down. I have a feeling this is going to Unusual Suspects us at the end, and a lot of these criminals are going to have ties to the whole thing. Anyway, I think Reddington was in love with Berlin's daughter and they either lived together with him being the only father she knew, or Berlin's daughter was already dead at that point and Reddington tried to "go straight" and raise her as his own. The real dad, the real bad guy of the whole show, comes after them to get her back, and somehow the house burns down and Reddington saves her and realizes he needs to go back to (or become, not sure the timeline) being a bad motherfucker himself to get this guy. And hides Lizzie with the other guy to raise her while he protects them from afar. And of course through convoluted misunderstandings and shit, Berlin thinks that Reddington killed his daughter.
In other words, I think Lizzie's real dad is the real bad guy of the show and we haven't seen anything about him at all yet. I do think that Reddington might be speaking metaphorically on that one point, where he said that he promises her father died in that fire. It is possible he really thinks he did die, so isn't lying that he knows of, but it is possible he's referring to the fact that by setting the house on fire and trying to kill Lizzie, he's a dead man walking. Either way, I'm fairly certain Tom was telling the truth about him being alive, and he'll show up later.
Hell, maybe it's Alan Alda, who doesn't realize who Lizzie is. I doubt it, but you never know, Alda does have a bit of a weird part to play in the show and you'd think they could cast just about anyone for the tiny role he's been given. There's definitely more to that whole story too, but I sort of think if Reddington knew it was him, he'd have been dead a long time ago.