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The entire "roach" incident supports Lily's belief, well I'd say it confirms Lily's belief that her mother had actually spent time in the Boatwright house. This was an important revelation. Lily sees roaches as unlovable, things that never go away, and things that cannot be gotten rid of. She wants to hold onto her mother, but her memory has become ugly..... she needs to know the truth, but she's afraid to ask.