Essentially the same as any other character in the game; throw out safe, low endlag moves that allow you time to react if you whiff or hit a shield.
When you're grounded, Dtilt is your best option. The hitbox comes out later than Jab, so don't use it if you need to hit someone fast, but it's the fastest ending move Lucina has, so if you miss you can immediately throw out another spacing option (Ftilt, Utilt, F-smash for the ambitious read) without be worried about punishes. It also gives you low profile so you can avoid some SH aerials from your opponents, and immediately punish with Utilt.
In the air, you want SH Nair or SH Fair. They're fast and have nice hitboxes that help you wall off your opponent or shut down their approach, regardless of height. At high percents (>100%), Nair 2 can get you kills out of Neutral at the ledge.
For mixups, Pivot Cancel Ftilt is a good ground spacer because of the sliding animation, and Utilt can catch roll-ins and short hops w/o the long endlag and commitment of Dancing Blade. Also, remember Shieldbreaker after you hit shield once or twice. Just the fear of the move is enough to have your opponent give up positioning. Lastly, tomahawk grabs. Any player with a basic knowledge of the MU will default to shielding on approach, so just grab em.
Things to avoid: Full hop aerials, as your opponent will have enough time to react and the vertical spacing makes you vulnerable to anti-air moves. Dancing Blade is good for catching rolls and spot dodges but if you get the wrong read and hit shield it's a free OOS punish (I play against an Inkling main, and Dancing Blade on shield -> Up Smash -> Lucina dies). Finally, Dair is a good mixup and a juggle starter if you get the stage spike and has a wide hitbox coverage, but one whiff or hit on shield and you're open to all punishes due to the endlag (Ness/Palutena backthrow, Wolf D-smash, Inkling F-smash, the list is endless).
I'm still working out my own neutral but this is what I've got so far.