Lily's main weakness is her desire for her parents' approval. Notice how she jumped at the chance when her parents summoned her to Scotland? This also feeds into her other problem of not letting others know about her emotions. She has her down points, but she actively hides it from others.
Lilly's traits tend to make more sense when you realize she's KS's version of the traditional Japanese (ironically since she has mixed blood) and the traditionally Japanese mindset often applies to her.
Here's a page containing some stuff about the Japanese mindset. A few things that catch the eye:
Many school children have said they have never seen their parents kiss. Young adults don’t talk about their boyfriend or girlfriend or lack of one and generally don’t like to be asked questions about their private life. In one survey Japanese university students said they considered a good friend to be someone who respects their private life.
Kimiko Manes, author Culture Shock in Mind, wrote in the Daily Yomiuri: “Japanese culture is not very open. When something goes wrong, a Japanese person frequently will not share the problem with others, instead suffering alone as they try to solve it. For example, suppose someone was not able to complete a task for a colleague by a certain date. Rather than explaining the nature of the trouble to the colleague, the Japanese person frequently tries to tackle it on his own....Asking the other party the reason for their difficulties would be construed as a sign of disrespect....The truth behind a problem frequently is not communicable, which can lead to bigger problems later. The Japanese reluctance to hurt or make the other party lose face overrides the temptation to rationally explain the issue at hand,.”
In addition, I remember a quote saying Japanese are not allowed to have an opinion until they're 50. This was a reference to the fact that Japanese are often expected to never question their elders or those with authority...even when it's justified.
)
.