A good Mega Man will shut you down with spaced fairs and projectile spam. And if you leave yourself open during this barrage, he will run up, grab you, and start some mean strings. Luigi's crap air movement leaves him especially vulnerable to Mega Man's uairs. And Mega Man falls too quickly to land some of the nice combos at low percents Luigi normally enjoys.
As for what Luigi can do in return, remember that fireballs cancel out Crash Bomb and Metal Blade, which can stop his spam and also clashes with his dash attack. But make sure you space them out! Mega Man can move surprisingly quick, so if you fireball too closely, he'll mess you up. As for approaches, SH dair beats his dash attack and run ins while also being safe on block. Cyclone can also get in and toss him up, letting you get the advantage. You can also bait out a fair and get him on the ending lag. If you get him off the stage, his recovery can be spiked by dair. He'll usually cover his recovery with a fair though, so watch out for that. You can also gimp him with your own fair if he's not recovering low, and after that his bad recovery means he usually won't make it back.
Honestly, you're gonna have to be a bit patient with Mega Man, like with all spammers. You're probably just being baited in successfully. Don't take the bait. They're just doing an elaborate dance and, while it seems impenetrable, it isn't. Just don't rush, pick your shots carefully, and space your attacks really well. Once Luigi gets inside, you can definitely bop him around as long as you don't run into his fair and bair during your follow ups. But again, pick your shots carefully, bait him out too, and don't be afraid when you're off stage going for a gimp.