Here's some simple things that may help. I have no idea how advanced or skilled you or your girl is, so let me know if this info is too basic
- You can't combo luigi, don't try it. Seriously. Be content with the single hits and retreat safely. This is key
- In general, don't rest luigi. There are few situations in which it is a good idea. Because of his awkward mobility and being floaty, you almost never get rest opportunities so don't try to fish for them at all. If you miss a rest, you'll be up+b killed at low percents.
- Don't let luigi be above you. Ultimately, his dair is a brutal kill move that will out-prioritize all of your options. If you ever launch him up above you, don't try to follow up. If you really want to maintain pressure, do it by positioning yourself horizontally to him.
- Remember that luigi can get a misfire off a side-b, so be cautious when ledge-guarding and stay a bit low so he'll either fall into your attacks or misfire over your head.
- Remember that luigi controls massive amounts of horizontal space on the floor because of his wavedash. Because of this, remember that throwing out attacks isn't as safe as you think it is. Be cautious.
- If you're really playing to win, an effective trick is to just not let luigi play his game. Luigi is great on the ground, but his floatiness makes him very vulnerable in the air. Don't stay level with him: if he's on the floor stay on the platforms, and vice versa. Make him jump around and hunt you down, and then punish him for it
Hope this helps. I have a buttload more information than this about this matchup since my main training buddy is a luigi main, but I kept things brief and simple here because I'm not sure how advanced the info you're looking for is.