Here's what I can figure, as a mid-level Luigi.
1. Thundershock stops the Tornado, and may be one of the ones that blocks the fireball. Can't remember. That limits our ground approaches to... not much.
2. Aerial-wise, as I believe someone said, bair outranges and nair outprioritizes most if not all of pika's aerials. If you must get into an aerial fight, try to be in front, since fair has the small start up lag and I believe your fair beats it outright anyway. Your best bet though is to *carefully* go for thunder to make us land (or if it hits, maybe die lol). But not if we're too close to the ground, then your asking for an fsmash to the face or shoryuken from the weegees with better timing.
3. Speaking of thunder, it is a real problem for Luigi's recovery, especially if we got up high enough (with nado) to get caught in the cloud. Happened to me, not much I could do about it. If we've got enough time we can wait and get past it (or try to hit you) with Green Missile, but of course we are then very vulnerable upon landing. Lag=pika fsmash.
4. Yay segways! Your fsmash out ranges our ground game, so if you can time it you're good. If you get in a spot dodge contest, I'm not sure which of our dsmashes comes out quicker but I know your jab does. Jab > dsmash may work.
5. Off the top of my head I think your recovery might be difficult as well. We'll try to bair you before quick attack comes out, or just regular edgehog if that doesn't work.
Summarizing, you've got the ground game and we've got the air. Unfortunately the air is where Luigi is normally playing. Recovery is about even, both predictable and punishable. Even though I personally have a little trouble with pika, I'd say for better Luigi's and Pikachu's it would be even or slightly in our favor, 55/45.
Try to find CR4SH, he fights a pikachu player more regularly.