I happen to be a Lucina main so I'll give my two cents.
For dealing with Uspecial gimps you can do two things. First, you can try getting better at teching and tech jumping, specifically. That's pretty hard to do online but I've seen plenty of other people in elite smash tech consistently (and I do it myself here and there). Second, you can try mixing up your recovery. Joker mains go low most of the time because a good chunk of the cast can't do anything about it. However, Lucina is one of the few characters that can chase you down there (to a certain extent) and I personally get a lot of mileage out of low Fairs and Uspecial stage spikes. Joker has a very flexible recovery, though. You can mix up how you recover by getting a lot of horizontal distance through his guns, and either neutral airdodging, double jumping over or countering an attempt by Lucina to hit you. Try keeping your opponent on their toes to avoid being predictable.
In neutral
First, make sure that you are on point with Joker's punish game. Joker's biggest advantage is that he can outpace Lucina in the punish game. If you two are winning neutral an even amount of times, then you should still be ahead since Lucina will only hit you once or twice per punish. If she's in the lead then you're probably getting outplayed in neutral so keep a cool head and adjust accordingly because you can always close that gap.
Second, you should focus on baiting and whiff punishing Lucina instead of rushing her down. Lucina wants to keep people at a comfortable spacing with her big hitboxes and poke at them for trying to get close. However, Joker has the tools to exploit her weaknesses. Joker has MUCH more mobility than she does, his moves are quick with little endlag, and he has a good burst option. Lucina's moves are quick and big but they're fairly laggy and they don't have a lot of active frames. If she whiffs any rising aerial or tilt, Joker can easily rush in and make her pay. Running Dtilt and dash attack are good because they are quick and Joker lurches forward. Focus on using your movement to be evasive and frustrate her into swinging recklessly. If you're getting hit a lot, then you're probably being too aggressive.
Third, use your projectile to keep her honest. In my experience, Joker's side-special isn't good enough to really wall her out, but it does keep her on her toes. If you find her getting too comfortable dash dancing out of range your range or rushing in, a side-special to the face will make her more defensive.
Fourth, mix up your landing options to avoid getting juggled as much as you can. Lucina gets a lot of mileage out of juggling with her Utilt or Uair. Joker's guns are good for covering underneath him but you shouldn't be too obvious since she can hit you from the side. Some other good options are fast falling while neutral airdodging, drifting away and directional airdodging, and using guns to move around horizontally. Use some combination of these options to keep your opponent on his or her toes. Countering also works but that can be baited as well so don't overdo it.
Fifth, when you have Arsene make sure you go HAM. Joker's hitboxes with Arsene are REDICULOUS and they will beat out almost any other character, Lucina included. Here's a link showing what I'm talking about
https://www.eventhubs.com/news/2019...nd-just-explode-size-when-his-persona-active/ I see a lot of Jokers mainly hanging back and using Eiha (yeehaw?), which in my opinion (keep in mind I'm not a Joker main), is a mistake. Like, you're just conditioning your opponent to shield and avoid you, so you actually help them camp out Arsene.
Sixth, Lucina is really hard to edgeguard but it is possible, especially with Joker. Lucina has a very quick Uspecial but it is very linear and you can break it down in a very flowcharty way. When she's at low or mid percents she can mix up what she does so it's fairly hard to hit her, but starting around 80 or 90 she gets sent far enough that she has to expend some of her options early and she has to drift underneath the ledge since she doesn't get much horizontal movement from her Uspecial. Pay attention if she either double jumps early or directional airdodges. If she uses her airdodge (Mr. E uses that quite a bit) then she can't really avoid a well placed attack and she can't act for a while. If she jumps then she can't move much at all until she uses her Uspecial. Guns, Nair and Bair are great options for hitting her deep offstage. Here's an idea of what he can get away with offstage
https://www.youtube.com/watch?v=AigE252GQyM
Well that's all I can think of. I hope that helps.