Who comes off better here, Lila or Annie?
Does Lila simply not follow the more technical description, or is she saying “but that’s not how to think of it, at a personal level”? I’m not sure we credit her with that maturity though.
BTW, I think the adoption has already officially gone thru at this point in the cycle, but it’s still more reasonable for Lila to say “my dad” in the first panel than try to use “your granddad”.
Comics I Don't Understand 
It could be either. But I’m inclined to say Lila just doesn’t engage with the slightly more technical medical description Annie gives, and thinks she is simply giving a correction.
It would help knowing the characters better — I rarely read Lila, so I only have a glancing familiarity with it, which, though it may be completely wrong, has me seeing it as one of those snarky, everything-is-irony strips, with Lila being mostly shallow and the humor being mainly to laugh at her, not with her. But that could be a totally wrong assessment. It’s really hard to tell from one strip.
It goes with the theme of Annie being super smart and Lila…not.
larK, I certainly agree there’s a kind of double vision in the way the strip regards the character Lila, though I’m not sure irony is the right dimension to see that under. and definitely not snarky or everything-is-irony. What they seem able to do surprisingly well is keep us (largely) sympathetic to her, on her side, despite showing her as irresponsible, unreliable, limited intellectually, willing to exploit her sex appeal to get ahead at work, and – rarely but significantly – sometimes even disloyal to her friends. They accomplish keeping us on her side by showing her as (almost always) very loyal to her friends, genuinely fun-loving, generous (with the right people), and although often skeptical of the rules still right-minded when it matters in a big or serious way.
So the big part of the campaign to habilitate her (I won’t say re- ) was to show her befriending, and eventually loving and adopting, this orphaned young girl leukemia patient, Annie. That doesn’t absolve her from making parenting mistakes, and sometimes talking down to Annie, even though as Targuman points out Annie is super smart and Lila not so much.
One thing that does seem simply ironic, and at Lila’s expense, is that she thinks her looks are very sexy, and this underpins her flirty attitude at the office. But actually, only the very old top manager considers her “hot stuff”. And that gets her some margin for error, but not a free pass to misbehave.
I’m really glad that there are people here at CIDU who follow this strip and can charitably interpret Lila’s behavior as being her standard (in-character, possibly adorable) imbecility. Before I read the comments, I thought Annie was being a bit of a nerd (although her hospitalization history may be responsible both for her unusual amount of knowledge, as well as the impenetrable vocabulary). Knowing nothing about the characters, I thought Lila’s reply made her seem like an utterly insensitive idiot.