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Did you ever get an answer to your question? The birthstone necklace was, indeed, for grandma. It represented the month in which they met; he said it was the happiness time of his life.

At the very end of the movie, the grandson visits a nursing home that his grandfather went to quite often. It turns out one of the patients is, indeed, a "Lillian," and she has been there for 24 years - ever since she fell asleep while driving and killed a man and his wife (Will's parents). He brings his grandmother to see her and grandma says she forgives Lillian, although Lillian is probably too far gone to hear her.

It is a happy ending. Good movie!