Wow - your Luigi is pretty good. I'm a mediocre player, but I think I can give some advice anyway...
@ 0:35: Luigi's B-air outranges Lucario's F-air, however I'm unsure
@ 1:10+: You dodged every single aura sphere after getting hit by that one. Awesome job, sir.
@ 1:29: O_O ... That was... like... ****nnnnnnnn... Awesome, sir, awesome...
@ 2:10: Yeah - going along with what Kigbariom said, you totally should be F-smashing more. :-P
@ 2:25: It looked like you had an unused tornado recovery left-over which you didn't use...
@ 2:55: Man, I make that mistake so often... the missed FJP. Good luck fixing that - although, nice job keeping the attempt where you could use the edge to cancel.
@ 3:08: THAT! DO THAT MORE OFTEN!
@ 3:30: Kig's advice plays biggest here - he was waiting for your recovery. You still had a tornado left-over to use if you undershot the sweetspot too.
In general:
Well, Lucario has a bunch-load of range, so I may be asking too much by saying this for this particular match, but try to space your B-airs a little better. I don't think I saw any connected B-airs except for one time at 1:20, where you managed to hit Lucario with Luigi's stomach area. Luigi's B-air is amazing - use it more (especially via reverse aerial rush). :-D
Work on your recovery a bit, you totally could have two stocked the Lucario player if you'd had some more trust in your tornado.
Keep those fireballs - they're better than mine. >_< Either that, or make them even better.
You have the same problem I have with slow attacks... You dodge/tap shield, become vulnerable a split second later, and get ***** by the hitbox as it comes out within the next ten frames (personally, I spot dodge and get ***** by the hitbox a few frames later, unless it's interrupted via a quick jab :-D ). Expecting quick attacks is a tough habit to break, so get started breaking it (I still haven't broken it <_< ).
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All in all, though, a fine and laudable Luigi. :-D