Luigi pwnz Falco.. period. Forget SHL.
1) SHL OMG
SHL isn't as hard to get past as it seems. It really doesn't matter if you get hit by a few lasers if you know how to follow up when you're close. Approach with WDs into shields. Your shield is important! You can shieldgrab and block lasers with it.
2) The Lcanceled Shine
Some Falcos are smart enough not to get shield-grabbed, so they lcancel aerials on your shield into shines. IMO, the best thing to do is WD back and
then forward again into a grab. If they jumped, then shame on them. Falco in the air + Luigi right below on ground = Falco taking damage. You can easily land an Uair on Falco from below.
3) Comboing Falco
Uthrow and Dthrow tend to work very well against Falco.Uthrow for chainthrows up to 30%. With Dthrow, however, you have a few other options. One that the Falco might expect is tech chasing. You can tech chase Falco wit h your Dthrow, it might even be clever to surprise them with an Uthrow into an aerial. Hitting them with that unexpected damage is a decent advantage. Secondly, After using Dthrow, Falco will land behind you. Do a reverse Dsmash (tap the direction that Falco landed and tap down on the C-stick). At some percentages, you'll hit Falco before he hits the ground, taking away his ability to tech. Falco just above and in front of Luigi = pwnage. You can do a few things. If he comes nearer to you (only at lower precentages, you don't want Falco to be able to jump) you can Utilt or Usmash and follow with Dair or Fair. If he's too far for another launcher, or you just prefer this way, then you can aerial him. As always, Luigi has a few different options of aerials here. You could do aan Uair into Nair, giving you another slight launch with some damage, but be careful as Falco might be able to jump after that. If you don't want to do that, or you're close enough to the edge that you can hit him off, then I'd suggest using Fair on him (Dair works too, but Fair gives you a bit more range to ensure your hit). ^^Basically do what you can do damage him, then get him off of the edge.
4) Edgeguarding Falco
Falco has two means of survival, neither being very good. He can use his OverB or his UpB. First, his OverB. You should be aware that Falco OverB is a meteor, so if you get hit while off the edge, you might die.Falco will only ever OverB onto the edge, or above you onto the stage. If Falco aims for the edge, then just Dsmash the edge. You'll launch him perfectly for another Fair/Dair off the stage. Plus, it's likely he's lost his jump. If Falco uses OverB above you and onto the stage, Run or WD if you need to to get under him and use your Utilt. Like the Dsmash, this will set you up to land another Fair/Dair and knock Falco off the edge once more. Second, Falco's UpB. To make things simple, Luigi's Fair > Falco's UpB. You have more priority. In fact, all of Luigi's aerials have a higher priority than Falco's UpB AND OverB. So you should have no trouble edgeguarding Falco. Besides what is mentioned above, a great way of edgeguarding is edgehogging (duh?). If he comes above you with UpB, then ledgehop into aerial (Dair or Bair to bring him offstage once more). If he OverBs onto the edge.. then he's dead. If he OverBs onto the stage, then Ledgehop to Wavedash to grab to Uthrow. Then use either Bair, a well placed Dair, or reverse Fair.
5) Launchers
Launchers own Falco. Luigi's best launchers vs Falco are the following:
-Unsweetspotted Nair
-Uthrow
-Utilt
-Dsmash (easiest to land in the combo Dthrow to reverse Dsmash)
-Sweetspotted Nair (<< this shouldn't be used as much as unsweetspotted)
Usmash has an odd trajectory, so don't use that too much.
6) Killing besides edgeguard
When Falco is at a high percentage, you don't need to bother with edgeguarding. It's quite simple, actually. A few simple combos are
-Uthrow to Fair
-Uthrow to Dair
-Dthrow to reverse Fsmash (same idea as Dthrow to reverse Dsmash)
Basically, be creative in the way you toy with the tiny minds of Falco players. Show them your moves, as Captain Falcon says.
LUIGI FTW