I agree that Red could fear that Lizzie might hate him if/when he reveals he is her father. Many people have negative feelings toward a parent who gave them up for adoption and stayed away, especially for reasons they might not understand or agree with. If it's true, we don't know the circumstances, and perhaps knowing those circumstances would be very traumatic for her. It might bring up childhood events that she mercifully doesn't remember. Also, if knowing Red is her father could put her in harm's way were it known by others, that would give her a major secret to keep, and having to keep a secret like that could be a huge burden to bear personally and professionally. One slip-up in the way Lizzie relates to him in public could jeopardize both their lives. Maybe even the threat that Tom and his organization poses is the end game here in terms of the Black List, and Red feared that if Lizzie knew, she might confide in Tom ... of course, that was when she didn't believe Red's warnings about Tom. At this point, she won't be confiding anything in her husband, but I can see that Red would still feel Lizzie is safer not knowing.