You outrange the hell out of Lucina. The obvious answer is to nairplane, and it works, but if you aren't spacing perfectly on your landing's she'll be able to punish. If you aren't comfortable going buster, try going shield when you approach at low percents. If you whiff a nair and she punishes, you can often eat the hitstun and get in a few utilts or a grab. Speed is naturally a great option, but I like to focus on speed nairs against Lucina, and only going for a grab on the occasional mixup.
Once she's offstage you can take a stock. If she recovers low just turn on Jump (or don't, generally if you save your DJ you'll be fine) and fair her. Get back onstage, and either drop off the ledge and bair or (if she was knocked far enough) climb back up, turn around and fair her again. If she double jumped before one of your fairs, her up-b likely won't be enough to recover.
A majority of my KOs on Lucina are from gimps and edgeguards. It's really easy to kill her this way, but its always a bit dangerous to smash her because of how hard she can punish with aerials, as well as the threat of counter.
Oh, and be a bit careful edgeguarding on your last stock. Twice now I've hopped down for the fair, ate a counter, bounced off the bottom of the stage and fell to my death. So depressing.
If I ever get a recording device I'll upload some replays. I've got some good Lucina games.
