Neutral:
Greninja outcamps Luigi with a faster projectile with more range than his so you're forced to approach him, however shurikens have a fair bit of ending lag, so it is possible to get to Greninja by using cyclone, but unless you're somewhat close, it's very easy for Greninja to shield cyclone and punish you for your troubles if they see it coming. Don't get too predictable with cyclones. Fireballs at close range can be useful to set Greninja up for a grab since if he tries shurikens that close, the end-lag is super punishable, so if he gets hit, shields or spotdodges, he can be grabbed, but he can still jump over it or roll to escape so it's not guaranteed
Luigi has to play defensively in neutral, the best opportunity for dealing damage to Greninja is shieldgrabbing a n-air. However, be cautious when doing that, n-air can push you away while you're in your shield, putting you a distance away from him and if you try to grab, you will miss and likely get grabbed yourself or worse. Be also cautious of Greninja going behind during n-air as similar things can happen. Greninja's F-Air and B-Air are safe on shield if spaced correctly, so be wary of that. Greninja's dash grab also has a great range and comes out very quickly.
Advantage:
Luigi can deal a lot of damage to Greninja out of d-throw which is great, however, his bad mobility often means that Greninja will usually be able to get away from him fairly easily with his superior airspeed and the assistance of Hydro Pump if need be. Try to keep Greninja above you as his only option to counter you is d-air, which will leave him vulnerable to an attack if it misses, or Substitute which has the same problem if it's not triggered. The moment Greninja is above you is the best moment to deal damage or get the kill, as hard as it can be to keep him there.
Disadvantage:
The best way for Luigi to get away from Greninja after being put in this state is n-air. Greninja can chase you down mercilessly and catch your landings with Up-Smash (though N-Air trades with it and results in only the first weak hit striking, keep that in mind) or a dash grab. If he shields your N-Air, you're either going to get jabbed or hit by d-tilt, which can be lethal at higher percentages due to it comboing into Up-Smash. It's better to try to break out of Greninja's juggling when you're both in the air, if you manage to hit Greninja with a N-Air while he's jumping after you for an Up-Air or whatever, he's going to be sent above you so you can use that as an opportunity to reverse the situation.
Edgeguarding:
This is pretty bad for Luigi. Greninja can edgeguard him well with B-air and Hydro Pump. One note about Green Missile, I believe it's possible for Greninja to use Substitute against it for edgeguarding as the move has quite the end lag when it hits something from what I've seen. Upwards Substitute can kill Luigi as early as 85% with no rage in Final Destination and leave Greninja completely safe to return even if he wasted his second jump before.
Cyclone helps Luigi recovery, but if the Greninja times it well he can hit Luigi during the end lag of the move which can result in death if you already used your double jump and you're not very good at the jumpless cyclone. Greninja can also stage spike you if you're below the stage or flat out kill you by timing a Shadow Sneak out of stage.
When it comes to the inverse, Luigi will have trouble keeping Greninja out, Shadow Sneak already lets him close the distance to the stage very well with little trouble due to the teleport, plus Hydro Pump mix-ups make him very hard to keep out. Be wary when jumping after Greninja for the gimp because you're at the risk of something like
this happening to you and possibly costing you a life.
So my take on the MU is that Greninja can outrange Luigi and chase him very easily due to much better mobility and he also can edgeguard Luigi very well. Luigi can deal more damage to him in a combo, but it's going to be difficult to really keep Greninja on a disadvantaged state. You guys need to make every hit count and try to get as much damage on him as possible before going for the kill. Greninja's smashes and aerials have a good amount of lag on them for you to punish, but be wary of his aerials since he can make them be safe on block and throw you off which will likely result in you getting grabbed.
Ideally you want to get Greninja when he messes up while on the ground where you can capitalize on his mistakes there more consistently, though if you find a good opening after he uses an aerial, go for it; once you manage to hit him, try to keep Greninja above as much as you can to deal damage. Edgeguarding Greninja is very difficult, but if you start to see patterns in how they're recovering, take advantage of them to edgeguard more safely. Be very careful when offstage because Greninja can get you dead very easily there.
Like I said before I don't know much about Luigi and his tools so I might be overlooking something, still, I hope I could be of help. This MU feels like quite the uphill battle for Luigi since Greninja is very good at keeping him in a bad position, but as long as you're pacient, you should be able to find the openings you need to win.