This is late I know, but still:
Matchup: Vs Luigi
I'll be quick here since most of the discussion on Luigi was already explained. I might update this later though.
Attributes: Luigi has one of the highest jumps in the game, a relatively faster dash than Doc, one of the worst air speeds in the game, and his trademark traction. Luigi's air speed helps us edgeguard him if he's knocked offstage. Luigi weighs in at 97, being very slightly below Mario and Dr. Mario.
Notes: In neutral, remember that if Luigi is using bair, nair, or uair to approach, he has to commit to those moves since they lack the quick ending lag of dair and fair. However, if Luigi doesn't autocancel any of his aerials not named bair or nair, he'll be stuck in landing lag. Punish him there. His bair is as strong as yours, but is very punishable if Luigi misses or is blocked.
Generally, Luigi has a better rushdown game than Mario and you. Don't give him the chance to throw you: If you get thrown, DI towards Luigi to avoid Dairs or any other setup (Not really avoiding, but reducing his potential followups).
I mentioned earlier that some Luigis think that Dthrow to Fair x2 is a true combo. It isn't at low percents, so UpB if they get greedy but be aware it's a true combo later on. Dthrow to fair to uair is a true combo, however. Also try to tech dair if he spikes you onstage, because dair can lead into other attacks.
As HeroMystic pointed out though, you need to watch out for Cyclone gimps, usually setup by Dthrow. Just don't get thrown near the edge, and try to DI towards Luigi in that case.
Luigi's kill moves are like yours. Bair is like yours, but way riskier if it misses. Nair is guaranteed from Dthrow, but it has to be fresh and around 160.
Luigi Offstage:
If Luigi is edgeguarding you, then try to avoid his bair and other aerial attacks. He might use Cyclone to read your airdodges however, so I'll need more testing on recovering on Luigi. Possibly you can trade with Luigi on Cyclone, but remember that the Cyclone gimp is followed by any of Luigi's attacks, not by strictly Dthrow. (Or at least that video shows)
Luigi's recovery is pretty varied. While his low airspeed can be a hindrance, Luigi is gifted with long, floaty jumps. Cyclone can be used after a double jump or mashed on it's own to greatly increase Luigi's vertical distance. Green Missile is used for horizontal movement, though it can misfire 1/10 in this game. Super Jump Punch is low priority, and moves Luigi up without any horizontal movement, but can sweetspot the ledge either way.
When you have Luigi offstage, it's easier. Despite his good recovery, he lacks high priority moves to discourage you from attacking him. You can always cape the Luigi Missile, but for Cyclone out of jump, watch for when Luigi is done spinning, and hit him with any move of your choice, preferably Tornado.
Securing the KO:
When Luigi's near the kill percents, here's what you can do.
Bair: The quickest, but don't forget that Luigi's bair is much like yours except it ends much later than yours.
Tornado: Offstage, Luigi is vulnerable to this move. Take out his low priority recovery and send him away!
Any other stuff (Smashes, UpB, etc): Always try to send Luigi at a horizontal angle. This'll force the Luigi to use his Cyclone to recover from below, and he's incredibly vulnerable after Cyclone ends. Luigi using Green Missile to recover horizontally is easily reacted to, though you'll just have to hope they don't get the misfire.
Tldr: Doc has better neutral than Luigi who has to wade in and out. Though, Luigi is better upclose and that Cyclone gimp
My Opinion: 40:60 or 45:55 being generous, since Luigi can kill us quicker near the edge than we can, though Luigi is pretty vulnerable recovering too. We need to focus on making sure Luigi makes mistakes while approaching since his neutral is iffy.
General Opinion: 40:60 - 45:55
Moves to look out for:
DThrow: This is self-explanatory. Luigi's throw is at a fixed knockback unlike Mario and Doc's, so he'll always get combos. Needless to say, just make sure he doesn't grab you in the first place or else you'll be subject to a million followups. If you get grabbed DI towards Luigi to minimize the amount of followups he can do.
Bair: Same deal as Mario and yours, but Luigi's can kill like Doc's, though it's ending lag in the air is atrocious. Anytime he misses this or is blocked, punish him. Please.
Fair: Luigi has really fast ending lag after this, not mention it knocks you away. Use something like bair or Tornado to stop it. As a side note, if the Luigi screws up and this is not autocanceled, punish Luigi.
Dair: Luigi's meteor is worth looking at for several reasons. It has really fast ending lag, so Luigi can spike you onstage and immediately followup afterwards. The second use is the other hitbox where you get sent at a diagonal angle. Pretty much you'll need to stop Luigi from using this when he's ready to kill. An USmash from below can sometimes hit Luigi, but you'll need to be away from Luigi in order to knock him out of dair. Once again, if Luigi lands without autocanceling you'll need to punish him immediately.
Nair: Luigi's sex kick is one of the strongest in the game, and sends you at a vertical angle, prime for juggling. Most Luigis will try to use it as an KO option at high percents because Boss likes to do that. Either way, KOs by nair will usually be setup by Dthrow. Because it'll usually be used for fishing for KOs, you should try to DI so that Luigi's nair will miss.
Smash attacks (Namely FSmash and DSmash): While FSmash is low ranged, it's great for KOing. DSmash isn't as powerful as FSmash, but it's incredibly fast and sends the opponent at a diagonal angle. Block this and punish Luigi.
Fireball: Luigi has a rare case of using a projectile that has little commitment to it. While it's not incredibly great, it can be used to annoy and pester you. Either way, because of it's horizontal movement Luigi can use fireballs to block a section of the stage. If you want to get creative, use your pills from a full jump so that they force Luigi to avoid it, hopefully making him move to you, but in neutral where he has to commit to something.
Green Missile: Luigi's side recovery has low priority and is easily caped. Tornado it, bair it, cape it, whatever you want. If they get the misfire.. prepare for it via cape or spotdodge.
Super Jump Punch: While Luigi can sometimes combo into it from Dthrow, this is mainly dependent on the opponent's DI. Either way, nobody likes dying from a Fire Jump Punch so try to DI away so that Luigi can't get the sweetspot. Really, you'll see this if Luigi is really upclose and you've messed up.
Luigi Cyclone: Cyclone is really something. It acts like a laggier but more maneuverable version of your Tornado, but offstage it can be used to gimp depending on the character's weight and floatiness. On stage, Luigi may use this as a surprise movement option. If that's the case, block it because when Luigi is done with the move, you have a lot of time to punish him.
Offstage though, Cyclone can gimp. Really, the ways you can avoid this tend to be either recovering high so that Luigi has to catch you, or using a combo breaker to avoid Luigi setting up this move.
When used for recovery, it can be mashed to gain some pretty big height. However, Luigi has to commit to this move when recovering so when it ends, Luigi is bait to edgeguarding.