The 33-year-old pop star releases her autobiography 'My Thoughts Exactly' in September and the 64-year-old actor - who split from Lily's mother Alison Owen when she was just four years old - is expecting the parts on him and his parenting will be a ''tricky'' read because she has been critical of him in the past.
In an interview with The Daily Telegraph newspaper, he said: ''Listen, man. I'm not made of steel. But I have read stuff that Lil's said about me [previously] and I've thought, 'Really? Hang on a minute. That's not my memory, not quite.'
''But, you know, it's tricky, and it will be tricky ... 'Because like I say, me, in her eyes, abandoning the family, is a big thing.''
When asked why he hasn't asked for an advance copy of the tome, Keith answered: ''She's not asked me to read it.''
The 'Shallow Grave' actor also revealed that Lily's brother, 'Game of Thrones' star Alfie Allen, is also pensive about what his sister may write.
He added: ''I know Alfie was very worried about it. And I said, 'Well, if you're that worried about it, you should ask Lily (if you can read it), and see if you can have final say on what's in and what's out.
''I have no idea where Lil will go with it. No idea, but, you know ... we'll see.''
As well as being concerned about the family dramas that could be included in the book, Keith admits he worries about his daughter when she chooses to speak out about politics and social issues, with her favourite forum being Twitter.
He said: ''It all depends on who she takes on. But I'm often thinking, 'Oh hell, you better weather this one, kid.'
''The thing is we're poultices. We bring out poison. And she is a poultice, and that poison will go towards her. And there's nothing I can do about that. I'd get worried if I thought MI6 were thinking she was so dangerous they'll have to bump her off ... But I don't think we've ever come to that.''