As you progress further in Pokemon Moon and near the end of the main storyline, you will have your chance at battling and capturing Lunala. Like many other Mascot Legendary Pokemon, Lunala makes for a very difficult capture. To start, odds are it will be equal or higher than most of the Pokemon on your team, sitting at a pretty decent level of 55. It will also probably be faster than most of your Pokemon, with a Base Stat of 97 (one of the higher Speed Stats in all of Alola). And let's not forget the offensive and defensive power it has, plus its exclusive ability that basically works like Multiscale, cutting the damage it takes at Full HP in half. Yeah, this thing won't be easy unless you're using a Masterball on it, which we don't recommend.
Here Are Some Tips For Catching Lunala:
Like most Legendary Pokemon that don't have the highest Level in-game, you should definitely only use Ultra Balls on Lunala, but only after getting its HP as low as possible. This can be incredibly difficult, since it won't have a problem crushing all sorts of holes in you team. And that's why you need to have more than the average amount of Ultra Balls, Revives and Hyper Potions.
False Swipe is also nice to have on one of your Pokemon, guaranteeing that Lunala will be left with at least one HP, should you have the TM or a Pokemon that knows it. Thunder Wave continues to work as the best status condition, since it's permanent (unlike sleep) and it doesn't cause Lunala to lose an HP.
And don't forget to ALWAYS save before facing Lunala. You are FORCED to capture Lunala (Nebby), no ifs, ands, or buts about it. It's a safety precaution, one that has worked since the first generation of Pokemon.
You can also use roto catch
Pshh...I caught my Lunala in a Quick Ball, they've always worked for me. Route 8's pokecenter, second dude at the counter, buy a bunch of them, they'll catch just about anything. See a pokemon you really REALLY want? Toss a Quick Ball right in the beginning of the encounter, you'll snatch it up without much problem, if there is a problem, then whittle down the pokemon's HP little by little with False Swipe. I have a Lurantis for that, and she's also got Ingrain, so I can whittle down a pokemon all I want and for every attack done to me (provided it's not a one hit KO) I stay in the game with a bit of a safety net. It would make shiny hunting pretty easy...if I had the patience for it.
Firstly, Lunala is a Ghost type Pokemon, so Normal type moves, such as False Swipe do NOT work on it. Lastly, it's capture rate is moderately low, that you can use Pokeballs to catch it once you lower its HP a little.
If you have a pokemon like Machop or Machoke use Foresight on it, then False Swipe will work. But yeah, you definitely won't need the Master Ball or Ultra Balls for Lunala