1) you should ask SBI for reasons as to why it has rejected your application for home loan
2) SBi would have rejected your application only if your title was not clear and marketable .
3) contact a local lawyer . let him peruse the papers mentioned by you . then based on legal advice proceed further
4) you can if you so desire approach another bank for home loan . if the sai bank also rejects your application dont purchase the property .
5) as per the gift deed mother had life interest in the property and sale by daughter lily during her lifetime was illegal
6) section 43 of transfer act protects interests of transferee when property has fraudulently been transferred by transferor ie lily in present case . when it is discovered that the transferor acquired an interest in the transferred property, at the option of the transferees, he is entitled to get the restitution of interest in property got by the transferor, provided the transferor acquires such interest in the property during which contract of transfer must subsist."
7) on demise of mother Lily acquired transferable interest in the property . it would protect the purchaser interest as lily had fruadelently transferred property but on mother death became owner of her share in property