Maybe I just haven't fought good enough luigis, but the MU seems like it's slightly in luigi's favor at worst. Luigi can do disgusting amounts of damage off of a single grab, which is his biggest advantage in the MU. Meanwhile, he has numerous options to be able to mash out of zard's few throw combos, however, it's not all bad for char.
Luigi has three main weaknesses in this MU:
1. He can be walled out. His moves are quick, but his ground and air speed are meh at best. He has short range and low traction, so he won't be running circles around us any time soon. His best (and only) option at mid-range is fireballs, which can be shut down by flamethrower.
2. Sheild push makes approaching luigi much less scary than you'd think. Perfectly spaced fairs on luigi's shield, for example, push luigi too far back for him to get the grab afterwards. This, plus his first problem can mean that luigi will have trouble getting in on zard, if we're willing to play patiently.
3. His recovery is limited and punishable. Flamethrower gimps are effective against luigi. Flamethrower stuffs his attempts to Side B and Up B back to the ledge. He might be able to pull out some shananigans with cyclone, but this can be punished with a spike if spaced/timed properly.
However, he DOES have obvious advantaes in this MU
1. He has a hard time getting in, but once he does get in, one grab can instantly net him 60%+. Not only can luigi wrack up damage quickly on zard, he has reliable kill setups out of grabs that can end our stocks early if we mess up. Playing this MU for zard is like walkin a tightrope, one little mistake and he can punish us dearly.
2. His moves have stupid priority. You have as much of a chance of challenging luigi's moves as you do marths.
We have to respect luigi's options and not try to play rushdown against him. Flamethrower, ftilt, and in some cases Fair are the best moves we have for challenging luigi's attacks.
3. Cyclone gimps.
This point is purely theoretical, since I've never been in this situation myself, but I've heard the bowser boards talking about this. Aparently cyclone gimps are a thing. It's not surprinsing considering the stupid amount of priority the move has. If possible, try not to recover low against luigi. The ending portion of fly does not have super armor, so a smart luigi can try to hit you out of your recovery with this. If possible, try not to waste your jumps when knocked offstage, you'll need them if put in this situation.
Overall, I'd say 4:6 in favor of luigi. It's a similar MU to MK in that he can do distusting amounts of damage if he gets an advantage, and can kill us early to boot, but has limited approach options, meaning that he can be walled out. Char should focus on playing hit and run in this MU. We wall luigi out while taking what hits we can, then use one of our many KO options to net the stock when the time comes.