One way to interpret the 'color of loneliness' in Twilight fanfiction is through the use of black. Black can represent the void that a lonely character feels. In fanfiction, a character like Jacob, when he realizes he can't have Bella, might be described as surrounded by a black cloud. His actions become more solitary, and his world seems to lose its color, turning into a monochrome of black, signifying his loneliness.
In Twilight fanfiction, the 'color of loneliness' could be depicted in various ways. For example, it might be the grayness that surrounds a character when they are separated from their loved one. The vampires in Twilight often experience a sense of isolation, and fanfiction can expand on this. It could be shown through their solitary hunts in the forest, away from the company of others, with only the cold moonlight as their companion.
The 'color of loneliness' in Twilight fanfiction might be a deep blue. Just like the cold, vast ocean that Bella sometimes feels she's drowning in when Edward leaves. Fanfiction authors might use this color to symbolize the depth of her despair. They could describe her world as being tinted blue, from the clothes she wears to the way she sees the landscape around her, everything reflecting her lonely state.