I don't own Harry Potter.
The first time Luna tried to cast a patronus was in her second year. Her things had once again begun to disappear, and wandering the castle had once again become one of the activities that she did most often, aside from classes and homework. That day she had been looking for the right shoe to her pair of sparkly, red shoes, the special ones that Daddy had insisted she get when he had heard that when you clicked the heals together a heard of flying monkeys would appear. Daddy had thought maybe the poor chap had gotten flying monkeys confused with the Nargles' larger and more substantial cousin, the Yougles, and had insisted that they try. No Yougels came, but they were probably just shy.
She had been looking for the shoes after they had gone missing. Her wanderings had led her out onto the grounds, because when the castle yeilded nothing, perhaps maybe the Nargles had gotten extra adventerous and hiddne them outside. Later she would note that she had strayed to close the boundaries of where the Dementors roamed. It had been cold outside, and she had only been wearing a light cloak; she had mistaken the Dementors' deadly chill for a more mundane kind.
It was only due to luck that she knew the spell at all. Ginny Weasley had asked about it in DADA after seeing Harry Potter perform it. As the Dementors' unearthly chill settled deeper and her thoughts became bleaker, Luna had tried to think of one happy memory.
She tried to think about her mother; all of the images became her father sobbing over a broken body. She tried thinking of her father; she saw a man quietly crying under the sheets at night and quicjly losing more of his grip on reality. Images of playing with Ginny and other friends became children jeering at her. Nargles and Wrackspurts became things that haunted shadows at night.
The incantation had came out barely more than a whisper. "Ex-expect-to p-patronum."
Not even a whisp of smoke had come out her wand. Only the fact that Professor McGongall had been close enough to hear her scream had saved Luna from having her soul sucked out.
It had stayed like that for all of her second and third years, no matter how hard she practiced. On an especially good day, maybe one where a first year who didn't know not to talk to 'Loony' Lovegood had asked her for directions or the Wrackspurts were less active than usual, she could manage a single whisp of smoke. When she asked Professor Lupin about it, he had said that she probably wasn't thinking of a happy enough memory.
In her fourth year, she learned he was right. She had all but given up on the patronus after the end of her third year. She met Ron and Harry and Hermione and Neville and the DA, and reconnected with Ginny. She made friends and memories. When it came time to try patronuses, a hare bounced happily around the room.
It was friends that she thougth of during the battle. When she was showing Harry Ravenclaw's diadem, she was internally praying for his safety. When she was throwing a curse at some Death Eater as she charged down the stairs, she was keeping a careful eye out to make sure none of her friends got hurt. When plaster dusted her hair from a crse just narrowly dodged, she was thanking heavens that it was her, not someone else.
So when he saw Dementors threatening her friends, she didn't even have to think before there was a hare driving the Dementors back.