He's her adoptive father, and, with just six weeks left to live with terminal cancer, he's put to death by Red. But it's not quite a mercy killing. It's Red wanting to make sure that Lizzie's adoptive father doesn't tell her the truth before he dies.
She already knows that she was adopted, so that's not the truth that Red wants hidden. Again, the overwhelming likelihood at this point is that Red is Lizzie's biological father. But that seems so clear that the truth is likely to be more, and the question is what more.
I'm thinking more than ever that a significant part of the answer resides with the husband, who just doesn't seem what he appears to be, despite Lizzie's faith in him. And, indeed, the best scene in tonight's episode nonverbally confirms that - at least to me.
Red sits next to Tom, who knows that Lizzie's father has died, but (apparently) doesn't know that Red killed him. Red waxes poetically about life and death, and Tom takes it in. But when Red leaves, we're permitted to see a look in Tom's eyes, an expression, that says to me that Tom knows more about Red than he's letting on. Indeed, I think Tom knows all or at least a lot about Red, and he's married to Lizzie as part of some sort of plan to ... I don't know, perhaps get Red, find out more about Red, though that depends on whom Tom is working for.
So we'll see what happens. The Blacklist continues to walk the edge, tempting with interpretations of its unorthodox, compelling story.
See also The Blacklist Debuts: Alias Meets Jay Z ... The Blacklist 1.2: Mysteries ... The Blacklist 1.3: Construction Site Heights ... The Blacklist 1.6: Truth and Enigma ... The Blacklist 1.7: Natural Immunity