Lily Potter was Not pleased, in fact she was murderously angry. Why did no one care for her son, why did everyone either see him as the Boy who Lived or a Mini James... or as a Freak in Petunia's Case...? Why did no one see the kind, extremely intelligent boy who had suffered so much... ?
Thanks to the Ritual she cast on her son weeks before she died, Lily's soul was bound to her son, acting as a anti Voldemort type Barrier. Unlike what that Idiot Albus thought, Love was only partially connected to the barrier and the same could be said for blood. In truth it was intent that was the most important part, you had to want to protect the person more then anything... simple love or blood was not enough. She created to allow anyone, even adoptive parents, to protect their children.
However something had gone wrong with her ritual, or rather the last part... her sacrifice. Voldemort's damaged soul fractured more, leaving a part inside of her baby which when mixed in with the abuse her son suffered made it very difficult to for her to establish a connection with her son. Which was a feature of her spell, one that would have allowed her to speak to her baby sometime...or at least grant him some of her knowledge...
All hope was not lost however, if someone removed THE Fraction of Voldemorts soul... she would be able to speak to her baby and pass on her knowledge to him. Occulemency was a specialty of her afterall. She was the one to teach it to Snape, whom was well known for the ability. She would be able to pass on this knowledge to her son and help him gain the freedom he so dearly lacked...
Lily had to bide her time... it would happen.. the soul fragment was already being pushed out by her presence and by Harry's strong will, it was only a matter of time. She would be ready... and nothing could stop her...
Ideas for this story... after the End of First year where voldemort passes through Harry, taking the Soul Fragment from him... After the Basilisk pierces him and he get healed by Fawxes, the energies purging everything from him that is negative...
When Voldemort is brought back... or a variety of other times...
You could make one up where Snapes tries Legimency on Harry during a class and Lily uses that to pass the fragment of Voldemort into Snapes Dark Mark... or when he looks at the Mirror of Erised and the mind reading powers it has removes the Fragment... be creative...