I personally agree that it doesn't fit into the main storyline, for me personally it's more because Frank is the one from whose eyes we see the events, switching perspectives with Lilly in between might be confusing.
I can't quite agree with your opinion about the memories though, yes what we saw was told to us for the most part, but I think it was quite heartwarming to see how Frank always took care of Lilly, the most difficult of the three. I also think that at least the scene when Frank taught Lilly to swim or when he took care of her when she was sick were new and gave us a better insight into the dynamics of the former Shavell-Oxtons. Even her nightmare, which I think was here, was never addressed and gives us an insight into how broken her own self-image and self-esteem was. I mean, we as viewers know that Shannon had developed an absolute dislike for Abby as she became more like her mother. But in Lilly's perception, she (Lilly) is not similarly unloved as Abby, but Abby is also favored over her, while Lilly is the worthless and incompetent one in her perception.
In short, I agree that there's little new here, and it's not necessarily important to the plot. However, it does help us get a better picture of Lilly's mental state during the 10 years her mother was married to Frank.
For some, not you, Lilly will continue to be the (formerly) unfriendly and stubborn brat, and there won't be much you can do about that. For us people who are interested in Lilly's past, or know or knew people who had a similar past but no Abby, Becca, or Frank in their lives, I think that has a different weight.