Some different Diana changes; Attempting to find Diana's niche.
From what it looks like, each assassin has their own niche.
Zed/Talon have the ability to jump in, assassinate and get out relatively safe. Akali has the ability to hide in her shroud and wait after going in. Katarina can go in and upon a reset, either get out or continue. She waits for low enemy. Rengar can jump in, and gets a speed boost upon escaping.
To put it really simply, every assassin has something that gives them the title "assassin."
Diana, while isn't listed as an assassin, has the kit of one but is in a weird place. She can get in and pop things quick but it's a lot harder for her compared to others and then the question comes, what's her purpose once she jumps in and doesn't pop an enemy in 1 burst? Her only escape would be to ult to a nearby minion. What if it's a team fight in the jungle? She jumps in, and gets a kill or gets them low. What then? She can't like be like Zed and teleport back to a shadow to escape. She lacks the damage Talon has to help solidify a kill. She can't shumpo away like Katarina. She can't hide in a shroud like Akali. She doesn't get the speed burst nor free resistances Rengar gets.
And her chase potential is limited to an awkward skill shot that is up every 4 seconds at max CDR. I understand she was originally nerfed because she had the burst of an assassin and the tankiness of a bruiser and that's a nono. So I'm not suggesting a damage change but rather to find her place.
Basically expand on the idea of her Lunar ability.
Make her passive boost depending if the enemy is affected by moonlight. Change her W to apply moonlight to the enemy hit by the 3rd sphere. Strenghten the slow slightly if the enemy if affected by moonlight. Allow her ult to gain small resistances/a speed burst if a moonlight stack in consumed by her ult.
This gives her a defined role of more of a bruiser than a mix of an assassin and a bruiser but below average in both regards. Not asking for all of those but just suggesting an idea for some changes for her skills.
With these changes, she has the ability to get in and affect the team as a whole.
Just some ideas.