I have so few straight ships and they all seem doomed to have only a few quality fics so you're welcome for compiling these
i’ve got a war in my heart: (by sable_tyger) https://archiveofourown.org/works/546991
Harry and Luna meet again, after the war.
Moonlight: (by TheFeistyRogue): https://archiveofourown.org/works/7905088
“Don’t do it!” Harry cried. “No, Luna, don’t do it... DAMNIT LUNA!” Luna grinned like the Cheshire cat, then disappeared.
Luna had jumped into the time stream. Again. And, just like last time, Luna had jumped with a one way temport, and so now he had to go and get her, just like she knew he would.
Why did these things always happen to him?
Higher Than the Sky: (by aeriedescent) https://www.fanfiction.net/s/12838569/2/Higher-Than-the-Sky
Luna’s easy swaying was different. Normal. In fact, he felt incredibly normal, like any other student dancing with their date. Even if he was Harry “The Chosen One” Potter and she was Luna “Loony” Lovegood; the least normal pairing of them all.
Like Invisible Strings: (by and_backagain) https://interhouse-fest.livejournal.com/40624.html#cutid1
The next night, unpacking his trunk, he discovers that he’s forgotten his spare set of quills, his last bag of Chocolate Frogs, and his Transfiguration book. Wrapped in a pair of his old socks, though, is a mirror, which Harry has snatched from the window the moment he’d seen Dumbledore arrive.
A Harry&Luna take on Book 6, in which Luna gives Harry a gift , Harry spends quite a lot of time determinedly not thinking about one thing or another, and Hermione despairs of his common sense.
freedom: (by kalypsobean) https://archiveofourown.org/works/2904266
Harry accidentally runs into Luna.
Not Right For Him: (by JJ Rust) https://www.fanfiction.net/s/3961411/1/Not-Right-For-Him
How will Hermione react when she learns Harry and Luna are together?
Luna’s Year: (by michelle-31a) https://www.fanfiction.net/s/1500318/1/Luna-s-Year
Harry and his friends gradually discover a growing friendship with a certain...
Play By Play: (by JJ Rust) https://www.fanfiction.net/s/5210147/1/Play-By-Play
In HBP, Luna did commentary for the Gryffindor/Hufflepuff Quidditch match. But what if she had done it as the girlfriend of Harry Potter?
Protection From Nargles: (by Arpad Hruntra) https://www.fanfiction.net/s/7352166/1/Protection-From-Nargles
Harry and Luna meet in the Room of Requirement. Mistletoe appears. Will Nargles be a problem?
Takes place during Harry’s fifth year, as he and Luna get closer. Basically pure fluff, largely consisting of conversations.
Burning Down Privet Drive: (by seriousblablah) https://www.fanfiction.net/s/12198211/1/Burning-Down-Privet-Drive
For his 21st birthday, Luna has a surprise gift. And it’s nothing Harry could have ever expected or predicted. Then again, nothing about living with beautiful weirdo Luna Lovegood is ever predictable, is it?
All So Quiet: (by hariboo) https://archiveofourown.org/works/227811
Luna and Harry in a quiet moment a few weeks after the war.
Fortescue’s, Or, What You Will: (by ms_worplesdon) https://archiveofourown.org/works/2825918
Luna resorts to drastic measures to get a job in the wizarding world.
Goodnight, Harry: (by museinmotion) https://museinmotion.livejournal.com/11760.html
Sometimes it’s the quiet companionship.
College Sweetheart: (by Cheerful_Clatter) https://archiveofourown.org/works/24576712
A chance encounter with a biology tutor leads university student Harry Potter into a relationship with the most interesting person he’s ever met. Yes, of course it’s Luna Lovegood. Time to find out what his parents think of her.
Bunnies, Bunnies, It must be Bunnies! (by ArielSakura) https://archiveofourown.org/works/14472747/chapters/33470199
Lunarry is Chapter 13! (every chapter is a different ship)