Delver was the reason Lily lived beyond her expected lifespan. She was only supposed to live for three weeks, but Delver's species possesses extraordinary healing abilities. Simply being held by Delver was what actually healed her—not the fruit.
When she arrived at the orphanage, Lily became sick because she refused to eat without Delver. As she grew older, she came to believe that Delver, her father, had left her because she was no longer a baby. That's where her desire to remain a baby stemmed from. She wanted to stay in Mori's class so she could remain small and be treated like a baby. She even refused to eat (possibly because the teachers kept telling her that eating would help her grow tall and strong). She was also heartbroken when the dress that had been sent to her no longer fit. To Lily, it was proof that she was growing up, and growing up meant Delver would never want her back.
SPOILER
Delver was the reason Lily lived beyond her expected lifespan. She was only supposed to live for three weeks, but Delver's species possesses extraordinary healing abilities. Simply being held by Delver was what actually healed her—not the fruit.
When she arrived at the orphanage, Lily became sick because she refused to eat without Delver. As she grew older, she came to believe that Delver, her father, had left her because she was no longer a baby. That's where her desire to remain a baby stemmed from. She wanted to stay in Mori's class so she could remain small and be treated like a baby. She even refused to eat (possibly because the teachers kept telling her that eating would help her grow tall and strong). She was also heartbroken when the dress that had been sent to her no longer fit. To Lily, it was proof that she was growing up, and growing up meant Delver would never want her back.