why does lily write a letter to her father only to tear it all up when she is done?

I don't think that Lily ever meant to send T-Ray the letter. After the phone call, she realized that she was done with her father. Speaking with him just returned her to the negative place she used to be in. Writing the letter was more of a cathartic experience, she wanted to purge her negative emotions towards T-Ray and think about her mother in her own way.