Lily's relationship with Deborah

Lily is very confused about her mother. All Lily knows about Deborah is that she shot her mom. After coming to Boatwright sister's house, August told Lily about what happened to her mother Deborah. Deborah married T.Ray because Deborah was pregnant with Lily. Later Deborah leaves T.Ray and Lily because she didn't like T.Ray. Lily feels unwanted because of this. But Lily is also confused about when Deborah returned, was she coming back for her stuff or for Lily? Would Lily be mature enough to handle the truth?