It could mean that in a fanfic (fan fiction), Lily (presumably Harry Potter's mother Lily Potter) is depicted as disowning Harry. This might be a very unorthodox or dark take on the Harry Potter story, as in the original canon, Lily sacrificed herself to protect Harry.
I haven't come across any extremely popular 'lily disowns harry fanfic' myself. Popular fanfics usually tend to stick to the more beloved aspects of the original story or expand on them in a positive way. A plot where Lily disowns Harry is so against the essence of the original story that it may not gain as much popularity. But in the huge world of fanfic, there could be some hidden gems or very specific - interest pieces that deal with this, but they probably don't have a wide - reaching popularity.
I'm not sure specifically about 'james disowns harry' fanfics being extremely popular. There are so many fanfics out there that it's hard to single out ones with this exact plot as being super popular. But in the vast world of fanfiction, any plot that involves a major relationship change like this could potentially have a following.
Well, it could mean in a fan - made story (fanfic), the character James disowns Harry. Maybe there's some sort of conflict or plot development where James, for whatever reason, decides to no longer consider Harry as part of his family or group.
One great fanfic could be 'Harry and Lily's Enchanted Bond'. In this story, Lily, being a fairy, might use her magical fairy abilities to help Harry in his adventures at Hogwarts. It could add a whole new dimension to the wizarding world as we know it.
In some fanfics, it could be due to a threat she believes she can't protect Harry from. Maybe she thinks that by leaving him, the dark forces won't target him as much.
Perhaps Sirius Black could also be involved. Sirius was Harry's godfather and was very much a part of Harry's life. His presence could add some interesting dynamics, like he could be the one who stumbles upon the magic that makes the meeting possible and then has to deal with the implications of Harry meeting his mother.
In a fanfic, Harry could be developed by showing how he copes with having his mother back in his life. He might have mixed feelings of joy and confusion. Lily could be developed by depicting her reaction to the modern wizarding world that Harry is a part of. She could be both amazed and a bit critical of some of the changes. This would give depth to their characters as they interact and adapt to each other.
Well, a fanfic about Harry and Lily Brerd could explore their relationship in various ways. Maybe it delves into their family bonds, or perhaps it creates some unique adventures for them. It could also show how they interact with other characters in the fan - created world.
Perhaps in this fanfic, Harry has been influenced by dark magic or some evil entity. This external influence could distort his perception of Lily and turn his normal feelings for her into hatred. Dark magic has the power to corrupt one's mind and change relationships in unexpected ways.