This is a good question, I theorize that the Nefertari Lili was in-fact romantically involved with Imu and that's why he came out himself and questioned Cobra about her. I think Nefertari Lili found out Imu's intentions too late and was responsible for the distribution of the poneglyphs. I think Nefertari Lili also ended up and died on Amazon Lily with Imu's kid BEFORE she could reach Alabasta. Thus the island is named in her honor "Amazon Lili"