One sad story in Naruto is about Sasuke. His entire clan was massacred when he was young. He had to live with this trauma and the thirst for revenge. He left his friends in Konoha, like Naruto who considered him a brother, to seek power from Orochimaru. This led to a long separation and many battles between them.
To write a really sad story, start with a character facing a profound loss or heartbreak. Build up the emotions gradually, describe the details of their pain, and show how it affects their life.
Unfulfilled dreams can also be a theme. Naruto has always dreamed of becoming Hokage to gain the respect and recognition of the village. If in a fanfiction, something prevents him from achieving this dream, like an unexpected injury or a political conspiracy, he would be extremely sad. He has put so much effort and hope into this dream, and to see it slip away would be a huge blow to him.
One popular 'naruto is sad' fanfiction might be the ones where Naruto is left alone in the village after Sasuke leaves again. In these stories, Naruto feels a deep sense of loss and loneliness. He has worked so hard to bring Sasuke back, and when that fails, it shatters his spirit. He might be seen sitting alone on the Hokage monument, looking out over the village that he is supposed to protect but feeling empty inside.
One common theme could be loneliness. Naruto often felt alone during his childhood, and at Christmas, this feeling might be intensified. Another theme could be sacrifice. Characters might sacrifice their own Christmas cheer for the greater good of the village. And also, the theme of unfulfilled wishes, as not all characters can have their ideal Christmas due to the harsh shinobi world they live in.
Maybe it includes the names of his lost friends. Since Naruto has lost many important people in his life, their names on the Christmas list could represent his longing for them during the holiday season.
His unfulfilled dreams could also contribute. Naruto has big dreams for the ninja world and for himself. If in the fanfiction some of these dreams are still out of reach, they could be on his Christmas list in a sad way. For instance, if he dreams of a world where all ninjas are truly equal but that hasn't happened yet, it would be a sad entry on his list during Christmas.
Rock Lee's story has a sad side too. He was a ninja who couldn't use ninjutsu or genjutsu. He was often looked down upon by others. But he worked extremely hard to become a great taijutsu user. His efforts were sometimes in vain as he faced many setbacks, especially in his battles, but he never gave up, which shows the sad but also inspiring part of his journey.