Well this is definitely a match up i've come across often (although more often as Marth than Lucina as he's one of my primaries, but despite that i think i can definitely help with this match up), and as i've used Ness and Marth/Lucina before, i think i can definitely help with this.
First off, when it comes to edge guarding Ness, this is something you (as Lucina) NEED to capitalize on, as in the neutral game, i think honestly Ness has the advantage due to his projectiles and grabs. He's pretty easy enough to Gimp anyway, first off, you should know that his Second Jump helps him go up very high compared to other characters and may help his recovery, although if he's launched far enough he'll still have to resort to his recovery move, which for Lucina is really easy to punish. Either:
A) You can go and attack/counter the PK Thunder orb before Ness hits himself, thus letting him fall to his death
Or the more safe option
B) You can walk off the ledge of the stage and time your counter/position so that if Ness hits you, Lucina will counter him and he'll be basically finished with the countered damage/knockback of Thunder Rocket, as it does ridiculous knockback and even if he does survive, Thunder Rocket won't have enough range to come back a second time.
PK Thunder takes about a second to aim before Ness will come back to the stage with THunder rocket, and it's pretty obvious when he's going to use it given that it's his only option. He could try coming directly upwards onto the ledge from below, but you can still counter that easily enough. Although it is a bit risky at higher percents for Lucina, but given how early Ness can kill, you might want to take the chance, depending on your situation.
As for dealing with his Neutral game, i think Ness definitely has the advantage here in keeping you out of range of hitting him and dealing damage to you from his safe range aswell. His
tilts arent much to note, other than his D-tilt can be comboed into a few hits if used repeatedly. His smash attacks are pretty good, Side Smash is really strong but has some start up, so you can block that easy enough. U-Smash has a hitbox that goes around Ness, and can deal damage even when being charged. Same goes for D-Smash, except it starts behidn Ness and covers everything below his hitbox. His grabs are pretty powerful and deadly at high percents (mostly U-throw and B-throw in this case), and a typical combo that you can't get out of with Lucina's hitbox if used at low percents is basically: D-throw > F-air > Ness Short hops/F-air again > F-air a third time. So watch out for his grabs all around.
His specials are also troublesome. You probably won't have to worry about Neutral Special (just stay away from it if he tries to use it, it can kill at 90%, and is risky to try to COunter and hit Ness with it, or punish him when he charges it and itsnot within range of Lucina) and definitely wont have to worry about D-Special (PSI Magnet), but U-Special and especially S-Special are the main obstacles Lucina has to get over in order to rack up damage on Ness. You can dash > shield to get in when he hits you with PK Fire but you will have to watch out in case he tries to grab you. Plus if you get trapped in the Fire, Ness can either hit you with his Side Smash, trap you with another PK Fire, or grab you for more damage. PK Thunder isn't really good as an approaching option on the ground, but when Ness knocks you into the air and he can't get to you easily, he'll typically juggle you with PK Thunder. You can air dodge it, but a good Ness will know to do a loop de loop with the attack so the tail of PK Thunder will trap you and then he can hit you with the actual attack. Although, while Ness may have the advantage on the ground, in the air Lucina/Marth's aerials take priority due to their speed and range, and can rack up damage while they can there.
I'd say definitely on the grounded neutral game, Ness definitely has the advantage, the only real thing you can do is try to get in and deal damage with the tilts/smash attacks when you can. Lucina/Marth's real advantage comes when Ness is in the air to rack up damage with their quick aerials and range, or when Ness gets off stage, as his recovery isn't really that good and he can be gimped by Lucina/Marth pretty easily.