Not sure if this has already been mentioned, but I had troubled with a ZSS matchup yesterday. If I approach her on the ground with down-b, she can just guess which side i'm gonna be on and will have a 50/50 shot at hitting me with her dsmash even if she doesnt attempt to read it. Approaching her in the air was also rough cause her up-b and up-smash outrange anything. My only options were to hit her with an aura sphere, which is annoying to aim since she has her ANNOYING *** GUN (yes im still a little salty) or approach from the air with down-b, but because of her range it's super easy to get caught. Once she's in the air it's not that hard, so I guess my question is how should I approach her?
I feel like you are getting caught up in the matchup and not focusing on playing your character. I've actually been working on dual maining these two characters specifically, because I feel the cover each other well and are both incredibly fun.
From ZSS's side of things, she lacks amazing approach options, so understand that shes probably going to be trying to outmaneuver you with speed, and catch you out for committing. Keep in mind that she gets very little off of grabs if you DI correctly so shielding is a good option that can be tough for her to deal with. Zss projectiles are slower than average, so powershielding is surprisingly viable, and can be clanked with. Try not to Double Team through the projectiles very often. Its a great option, but the problem is it's too good of an option and opponents will punish it very quickly if you do it too much.
As for approaches, as I mentioned, she doesn't have great ones so she will likely be looking to bait and outspace your approaches and punish them.
I mentioned I feel like you are getting caught up in the matchup, because it seems like you are relying on lucarios speed based tools to assist in keeping up with zss and getting punished. Try playing a bit more defensively. Uncharged aura sphere, pressure space with fair, and when you do go in, go in with guaranteed safe things. You said once she's in the air its not so bad, so I'll speak to grounded game more.
Dash Attack is a great combo starter, and with proper followup, you can make it safe on shield. Shffled Fair > Force palm also works great on grounded opponents.
If you are going to go in with DT, make sure you have a charge. You should be able to cancel it into a tilt while you still have intangibility frames from DT, leading to no more eating dsmashes.
Hope that helped!