I feel like you were playing peach in the vids, not lucas.
You were doing what you always do, but that happen to not be playing to lucas's strengths.
In particular, rushing from above with Dair is a weak choice due to the telegraphing hitboxes in both the dair and Fair.
I see Fair used more as a follow-up option from you, but if you use it outside of that, it would be wise to use it as a defensive measure in conjunction with retreating to get the most range out of it.
Your autocancelled nairs are great, I think I took that from either you or Galeon at some point, because it hurts bad players so hard. The problem being that most out of shield countermeasures are just better than another nair. As a result, I would advise ending it one or two nairs before they plan to punish and landing with a jab combo. Once again, this strategy is not terribly difficult to counter, but I find it more effective than another nair, which is considerably slower.
You use Uair for exactly what it's good at. Kudos. Note that this hitbox does not telegraph like the fair or Dair.
I also like how your recovery game was varied enough to matter.
TL;DR: I like your execution, but not your strategy. Lucas isn't good at using pressure as a main strategy throughout a match.