Meta is a tough counter to Lucas. Here's the rundown on the matchup.
Three Rules of Meta Fighting
1) PATIENCE.
2) Create Opportunities
3) Recognize Patterns
The first Rule of fighting Metaknight is patience. The idea behind a good Meta is to form spacing patterns with his low lag attacks, like F-air, F-tilt, and Downsmash, while he builds damage and sets up for a KO with a Downsmash or Up-B. Don't give him the hits. When meta is in the air he can't grab you or chase you horizontally very well so use your roll and shield to your advantage. When he attacks you on the ground, you can generally shield and retaliate or move away effectively, and I'll get into more on avoiding his patterns later, but for now, just avoid getting hit. Once meta gets a good hit on you it'll pop you up and you can take a lot of damage if you don't play your cards right in an aerial battle. So being VERY patient, taking your time, and camping meta is KEY. You have a stronger projectile game and that is your damage edge.
As Meta attacks you you'll find that you can't just run forever; you have to land your kill moves. However, if you can fluster him with PK fire, it may open an opportunity for an 80% U-smash, and you should almost ALWAYS take a gamble if it will result in a kill for you. A good kill setup against Meta is if he misses a dash attack or laggy attack and has a habit of rolling, quickly run behind him and plant a downsmash. The gamble is you getting a kill or an edgeguard opportunity against him getting a few punishing hits in.
Of course, throwing out attacks into space is going to get you chipped away into oblivion. Metaknight has weaknesses, and for the most part, they are his ground attacks. Meta's ground attacks have high returns when they land; the U-smash and D-Smash especially, and his F-Smash and F-Tilt are both low lag forward-hitting attacks that you will not be able to space or beat out effectively, and down-tilt is great for pressure and can build good damage, but while he's doing a ground attack, he cannot move away and space, and this will often be your opportunity to strike. In order for you to be prepared to strike, however, you MUST recognize his patterns. Think of it like a Boss in Mega Man; you must spend time dodging attacks and when the boss presents and opening, inflict maximum damage!
A few examples; I've played Metas that downsmashed after almost every attack and downsmashed after half of their downsmashes. I quickly learned that running at them after a F-smash or F-air would just get me smacked in the head, so I adjusted, ran forward and shielded the downsmash, and followed up with a fast N-air which would open up further damage opportunities, mostly tilts, and I could grab my KOs when I needed them, but then I ran into a Meta with a surprising trick; he would downsmash me, and sometimes, Up-B out of the downsmash and knock me off the stage. I got ***** for a match and a half before I caught on, but after a little, I started rolling away occasionally after the downsmash, and then I could plant a quick stick in retaliation to his Up-B (after I dodged the come-down attack as well). I ended up losing the set anyway, but it just goes to show how you can adapt to any situation.
Further tidbits of info:
PKT2 will beat out almost any attack that Meta has, don't be afraid to plant it straight through his aerials, so it's good to use in moderation.
Meta's Dash attack can be shield dropped into a stick.
Build damage always, build it until your f-air can KO. PK fire is your unholy tool of camping in this matchup, I swear to satan I do at least 50 damage a stock with it. Remember to do it low when you SH it. The more opportunities you can get to safely build damage, the better you'll be, because your upsmash is butt slow and hard to pull off so you want stick and dsmash available.
Speaking of dsmash metas will jump into that if you stand on a platform like dragonflies on an Indiana windshield.
Other than realy clear opportunities, don't use your stick. One, it's too short ranged to be effective, two it's kinda slow, and three you don't want diminishing returns to kick in, you need every ounce of tree branch power you can muster.
Grab combos are good (see combo thread for details) and you can KO with shield grabs at high percent.