Final answer:
The mother wants Lily to become a mother in the future based on her desire for motherly love and presence.
Step-by-step explanation:
The occupation that the mother wants for Lily is not explicitly mentioned in the provided information. However, based on the given excerpts, we can infer that the mother desires for Lily to become a mother herself in the future.
Several quotes from the text suggest the longing for motherhood, such as 'I want to be a mother to someone, and your children need a mother' and 'I was a little boy when she left, but though I am in the High School now and play in the school orchestra, I would rather see her than do anything I know.'
This indicates a strong desire for motherly love and presence. Therefore, it can be concluded that the mother wants Lily to embrace motherhood as her occupation.