Since I've played both of them (
on occasion and
as a full-time main), what exactly can I say about her?
She lacks a tipper, obviously meaning her strength is equal throughout her sword. This makes her weaker compared to Roy up close, but she has consistency, meaning you can space your distance or get close.
Since Lucina has more range than Roy, you can try practicing your distance between yourself and the opponent. That kind of defensive play style is safer for her than getting her up close offensively. But then again getting up close offensively is technically how I play her so she can work adequately in both.
If I also recall, a fully charged shield breaker performed aerially also pushes her forward, so be sure to keep that in mind when you're knocked off the stage because I believe it helps in her recovery back up the stage.
Jab 1 should also have good follow ups into anything you put into after. Like a f-smash or f-air for example once you did a jab once. Personally, I like to use Jab 1, down tilt then f-air.
I may be inaccurate in some of my info (bad habit of mine at this point), but for the most part I'm confident that most of what I said should work for you. You made a good choice in picking her up, and I encourage the thought of practicing her. Good luck and I hope you enjoy picking her up!
EDIT: Also, you might find that her up-b helps her escape jab lock situations like Little Mac's or Corrin's.