Honestly, I think it's an oversimplification to say we win if we keep Luigi in the air. Luigi is an incredibly slippery opponent that keeps you on your toes, he's very difficult to reliably combo and can get huge rewards off of a trivial punish.
The trick with this matchup is to remember that Luigi, like Pit, is a punishment demon. His mobility is godawful and he doesn't have very many strong moves in neutral, so he needs to exploit any and all weaknesses to get ahead. His grab is notorious for the d-throw followup combos it enables, up to and including f-air strings and the infamous 'nado: a single grab can result in upwards of 30% damage if discretion favours the green fellow. Even DI isn't an ideal option, since Luigi has a variety of followups to ensure that, no matter where you go, you get punished for it.
So we know Luigi's punish game is insane. He can easily dominate the neutral if you let him, with fireballs served every which way to force us to either try to out-camp him with arrows (risky, since Luigi can camp us out more conveniently than we can him) or approach. If we approach, we're in Luigi's element: now he can work to get the punish, and most importantly, the burden is on us to regain control of the set. Luigi loves it when his opponent is under pressure, as he can control the pace of the match with fireballs (a weak projectile that can nevertheless be spammed with ease, which makes mid-range options near-invalidated) and close-range options (grab is the obvious choice, but he has good frame data on his jab, f-air, b-air and n-air too, so watch out for these moves). If you really drop your guard, he can even seal the stock with a sweetspot up-b: essentially Jigglypuff's Rest with less endlag and moderately weaker kill power.
So how do we counter Luigi? Well, the good news is that, even though he can freely dominate the neutral if he's successful with his pressure tactics, he's very easy to exploit himself and has very few options out of his element. In the air, Luigi's only real answer is n-air (this is important, of course, I will get back to this in a moment), otherwise he's pretty easy to juggle. While it'd be naive to say his neutral game requires him to be within grab range or that that's his only viable option, he can himself be punished if we force him to approach instead. His fireballs, as mentioned, make it difficult to approach and our arrows only go so far to catch him out, so we need to get creative. If we can powershield his fireballs and force him to backpedal, he can end up totally free for a grab, which we can get decent mileage out of too; furthermore, because Luigi uses the 'nado a lot (especially as a d-throw followup or to punish our landing), we can get a feel for when he's going to use it and then shield-grab him from it. 'Nado may have favourable priority and does intense damage, but it's incredibly unsafe on shield, so a brief observation of when and how to best punish the 'nado can be a worthwhile investment indeed. You can, in theory, side-b to punish it, but I'd be very wary of this: 'nado's hitbox has a ton of distance to cover if it travels horizontally, which means it can hit you on the final frames when side-b's super armour dissipates. Just shield it and followup however you feel comfortable.
This is a very important point I need to mention, which applies to every stage of the match: beware reliance on combos! Luigi's n-air is essentially a "get out of jail free" card for combos, since it can come out between hitboxes and sends the target vertically. Luigi, as I mentioned, is a slippery opponent and his habit of punishing even the briefest drop in defence means we can never get too comfortable with our combos. Focus instead on punishing when appropriate and be sure to respect Luigi's options, because going full-on rushdown on the green fellow is a surefire way to get bodied.
Off-stage, we have a clear advantage so long as we steer clear of the 'nado: his recovery is decent if he uses up-b or 'nado in conjunction with side-b, but the side-b itself is criminally easy to intercept, either with an aerial or just with a kamikaze jump in front of it. It can discharge on occasion, so be wary of the kamikaze method if other options are viable. The 'nado itself can make interception dangerous, but fortunately it's only a viable option if Luigi is right below the ledge. Our job is to therefore keep Luigi as far away from the stage as possible: a good gimp can force Luigi into a position where he's just unable to recover! His edgeguarding game doesn't have much in the way of options either: except for fireballs and, if he's feeling bold, the 'nado, we should be able to go deep and recover quite neatly.
Overall, I think this matchup is tricky but bearable. I wouldn't say it's too far in either party's favour, but it can be very difficult for us to capitalise on our otherwise ubiquitous combos in this game. We need to respect Luigi's options and be able to return the favour whenever we get the chance to. It's a war of attrition, but if we persevere and fight with discretion and finesse, we can win it.
