With the new guidelines, a bit more effort in breaking it down by stage, and a lot more ambiguity:
Luigi vs. Sheik
Final Destination <
Battlefield <<
Dreamland <
Fountain of Dreams <<
Yoshi's Story <<
Pokemon Stadium <<
Sheik kinda ***** Luigi overall, and even more so when she has good platforms to work with. Dreamland's platforms being high is actually a good thing here for Luigi instead of a bad thing since Sheik can't short hop onto them.
Luigi vs. Falco
< for all
Platforms let Luigi be more offensive, as they let him move horizontally in the air (sort of), but they also let Falco be more defensive (since jumping on platforms tends to be quite safe) and combo Luigi a bit better. So, a solid < disadvantage all around.
Luigi vs. Marth
< for all
Marth beats Luigi, but it's not too bad, since he can hold his own vs Marth in the neutral game. Luigi does the best on Dreamland, but even then I wouldn't be comfortable saying that it's closer to even than Sheik vs. Fox.Luigi vs. Falcon
< for all
It's closer to even on the Yoshi's and FoD but not quite. Falcon outcombos Luigi in this matchup, and his aerial spam is more than adequate to defend against Luigi's approaches, especially when he has room to run.
Luigi vs. Ganon
< for all
same as above. Don't know enough about this matchup