I watched the vs. Ike.
You need to punish with F-smash instead of PKF. Also, edgeguard more with bair/dair. You overused PK Fire, especially since you didn't SH it.
punishing with Fsmash may or may not be a good idea based on %. at high % punishing iwth Fsmash may get the ko, while at low % punshing with fsmash may just be a wasted opportunity to get more damage done, diminishing your Fsmash power.
For example:
at 0% ike would get hit by Dsmash multiple times possibly all three times.
that could maybe get 30% off if you were to punish with dsmash(a move that isn't that reliable for killing), where as if you were to use FSmash (a very reliable killing move) it may only get you 14% and a missed oppurtunity.
Now same moves at high %.
if you were punishing for the kill and you knew either move would do, you would go for the faster/safer killing move for the punish, Fsmash.
don't quote me and say Dsmash is a reliable punishing move (besides against people that roll/spotdoge often), that was just an example of how you could get more damage done.
OK, for the critique of your lucas:
no offense to you, but i try to be as concise as i can when i critique something. So, from what i saw you played like how i used to play with lucas 4 months ago. You spam Pk fire wayyy too much. you use it to punish whiffed moves while they are right next to you, to approach, to bait an approach (nothing wrong with that) and just to rack up damage (nothing wrong with that either, but you hae more than just PK fire). PK FREEZE IS NOT A GOOD MOVE. it is easily avoided and punishable, and you should only use it a few times a match, if any. you don't have enough ftilt and jab. they are fast and can set up for more moves and combos. you should mix up your recoveries. when you are high, magnet pull is not the only way to get back on stage, and doing it too often you will become predictable (as magnet pulling has a very predictable trajectory). you can just float back magnet pull come back with an aerial/ airdodge, or even PKT2 back on when they aren't expecting it. Lucas' recovery is pretty good and you aren't using it to it's full potential. granted i'm not either because i'm not the best lucas ever, but i rarely get gimped. You fast fall everything which is not always a good idea. dair has ALOT of lag is you fastfall it incorrectly and Tyr_03 has a guide on the Dair i suggest you read it. it's a great move for lucas. when edguarding, you have choices once again. if the opponent is recovering high, Pk freeze can for an airdodge and mindgame opponents, and Bair is also a good choice. when recovering low you can pk fire if they are too close to the stage to lead into a bair spike or into a Pkt gimp, which is a really good edgeguarding tool. btw don't PK freeze when a oppnent is recovering low, because it doesn't reach down low enough.
sorry if i sound angry or mad or anything, i'm just really blunt when i try to help others.
I would say use grabs less, it's very punishable when it misses and they're generally not as good as Ness' throws anyway. Also, I think you shouldn't give up on PK Freeze just yet... I'm a PK Freeze fiend, and I think it's good for mind games near the edge and just raw damage at low percents. Though when fighting more difficult people, maybe it would be wise to use it less.