EDIT: With the new shield-stun implemented in the patch, some of this info may have changed.
How are Ness and Lucas keeping you out, respectively (I'll be assuming Zair and Side-B, but correct me if I'm wrong)? They seem similar but they're very different characters and have very different playstyles, attacks, approaches, and zoning options. I have experience playing as both these characters so I'll go over the points I know of and see if they're any use at all.
Zoning:
Lucas's PK Fire and Zair are arguably more of a problem than Ness's zoning tools since they're so much quicker and safer to throw out. Against Lucas I'd be patient, get in your shields where you can. Don't get conditioned to shield too much, though; a good Lucas will grab you in an instant and you'll be eating serious percent. So mix up your defensive options, using floats, rolls, spot-dodges, and air-dodges to avoid his attacks without shielding too much. Take it slow, and make your punishes count when you work your way in. If they're relying mostly on their projectile game, try to prioritize putting them offstage over damaging combos. You're much better off edge-guarding them to death from a lower percentage than you are doing some damage and then needing to chip away at the wall again, especially since Peach's edge-guards against Lucas are pretty strong once you get rid of the tether option (more on that later). This sounds kind of not fun. It really isn't. But it's the best advice I've got against a really campy Lucas, or any other character.
Ness's zoning options are a lot worse, since PK Fire is a lot less flexible of a move. Aerial PK Fire will only land safely if used out of a full hop, and even then he's vulnerable in the air after he fires the bolt. It should be pretty easy to punish after a quick shield. On the ground is another story. Ness's PK Fire is not exactly a good spacing tool/projectile, mainly because it's so slow and shielding it will generally get you a good punish if you're on your toes. Ness usually uses it to net a punish off of an unsafe commitment from far away. Don't mindlessly chase after him on the ground, he'll turn around and roast you. Float destroys grounded PK Fire. You don't need to float very high to avoid it and you can probably just drift over to Ness during his end-lag and slap him silly. Just be careful you only float over when you know he's going to PKF (or even better, practice doing it on reaction, which is not as impossible as it sounds), as his aerials are pretty good for challenging float approaches. Now that I think of it, side-b or float side-b might be a good way to punish Ness for a PKF at max distance, but I'd need to test that.
Chasing Them Down:
This is kind of an issue. Peach isn't very good at chasing people. If you're looking for a burst movement option to catch a foe that's running away, your two options are dash attack and side-b. Remember that sometimes you can't just punish a roll on reaction. They're pretty good in this game, so you need to read them. If you get enough of a read you can even go for a grab, which usually puts Peach in a pretty good spot. As far as dash attacks go, Ness's has some pretty good disjointed range, is decently fast, and sets up for juggles, but it definitely is punishable on block if he hits your shield with the first or second hit (not sure about the third; drop shield into side-b might work against a fully-spaced dash attack). It can't really be spot-dodged due to its three hits, but its one of those moves where rolling behind it sets you up for a nice punish if you know it's coming. Lucas's is rather slow, has less range, is more unsafe, can be spot-dodged easier, and is essentially terrible for approaching. He takes time to wind it up. You can see it coming from a mile away. If they're running at you with this, just dodge it or shield it and then hurt them.
Up Close
I'm not sure what you mean about Lucas having safe up-close attacks. The only ones I can think of are jab and sweetspot ftilt, and they don't really get him much as far as pressure goes. All his aerials are at least sort of punishable on shield, since none of them autocancel out of a short-hop. Dair needs to be full-hopped and doesn't connect properly, fair is pretty unsafe out of a short-hop, bair even more so, nair is pretty easy to punish if you shield all the hits since it doesn't cause a lot of shieldstun or pushback, and uair is tiny and no sane Lucas player will ever use it to attack your shield because they'll get messed up before they can.
Ness is another story. His grounded options are nothing to write home about, but no Ness player uses those because every aerial of his is freakishly safe out of a short-hop and on shield with the exception of fair. But for the most part his range is pretty puny. Treat the situation like this: Ness's only ranged, disjointed attack is forward air, and that's really unsafe on shield. Ness's only safe attacks are uair, bair, and nair, and all of those are pretty tiny when used as approaches (except bair which sort of has a disjoint but Ness won't approach you with bair because there are better options). So--this is the tricky part--you get a read on them. Shield will beat out fair. Your fair should beat out pretty much anything else. It doesn't open up combos, but I promise Ness will stop throwing out random aerials if he gets smacked in the face repeatedly for it.
Edge-Guarding
Toad blows up PK Thunder, but odds are you knew that. The MOTHER boys' main strength for mixups is their double jump. For Ness it's a pretty simple matter. His double jump is really good but can't sweet-spot the ledge, so he basically has two options: air dodge onto the stage (defensive choice) or cover his jump with a rising aerial (offensive choice). Both can be predicted and punished pretty easily when you pick up on them. Keep throwing him offstage until he's out of a jump, and then go to town.
Lucas is trickier to edge-guard since he has one of the better recoveries in the game. His double-jump is similar to Ness's, but Rope Snake makes things tricky. If he's going to tether, float over the ledge and threaten him with dair or a z-dropped turnip as he's reeling in. All of Lucas's aerials are much easier to beat out with a well-placed fair or bair or nair, so he likely won't be doing rising aerials or picking an offensive option. Keep knocking him away until he needs to up-b or he'll die. Lucas's PK Thunder goes much farther than Ness's and isn't shortened by running into things, but the upside to this is it's not nearly as scary. The projectile is slower, giving you a larger window to mess with him while he's steering it into himself. The hitbox around PK Thunder 2 is a lot smaller than Ness's, making it easier to challenge with fair or bair or nair. If you do get hit by it, it doesn't mean instant death at 20% like Ness's does (but try not to get hit all the same, it's much easier). Plus, it's even more important for Lucas to aim for the ledge at all times than it is for Ness since he goes into about a million years of end-lag if he lands on the stage. He's pretty easy to mess with once his tether is out of the equation.
In general, dair and fair can beat out air-dodges, but Peach has probably the best option of all: wait. She has a float; she can take her time. If they airdodge, just wait it out and hit them afterwards. Ground-float dair can cover the ledge from onstage and can stage-spike sometimes if it connects.
That was a bit more than I'd been meaning to write, but I hope at least some of it helped! ^_^
