I hate this MU, I only beat pocket foxes (I lost to a fox at Genesis 2 named Pink in some friendlies though after getting a good lead one time iirc, ugh such a dumb char w/ the boring looking chip play, I'm just being salty I guess haha) because they don't account for spacing fox properly (like you do in Melee, you keep about the same space, except in Melee you're zoning Fox's nair usually instead of his dash/SH mixups). If they're good they'll just wait you out and then kill you later. Basically my strat after seeing TKD murder a lucario (no offense to Ice, he's good, but TKD just knows the MU too well), is half of the time to give Fox a whole lot of room and make footsies and bait doing a lot of full hop out of SH laser range and juuuust beyond normal dash punish range, and make yourself look sorta punishable, lots of foxes like to run in on punishable looking stuff with a SH AD -> grab, uair, running usmash, utilt etc., and if you're full hopping and giving fox a lot of room, most conventional foxes that don't know the MU will whiff a lot of things trying to get to you.
If they're smart though, they just push in a little more or fully commit to camping, which sucks frankly.
Everything about this MU is dumb, fox just does his normal thing, Lucario runs ragged trying to get a punish in, Fox unlike other chars doesn't have a lot of problems landing, which is hard to abuse or zone vertically. dair oos is actually a decent punish for blocked stuff b/c of fox's more close range stuff, but it's only a punish strictly speaking. Fox has faster CQC, etc. If for some odd reason Lucario lives past usmash/uair kill percents, Lucario's aerials become safe enough on block sometimes, depending on percents, but it's otherwise pretty tough to properly put aerial pressure on fox.
Unlike other spacies, he's not really prone to getting edgeguarded as hard as the others.
If the fox has an AD habit or goes autopilot w/ dair and doesn't wait to see where you SDI and whatnot, you can sometimes get a jab in. Strutterstep smash can sometimes be useful on fox while he's on the ledge trying to get back onstage.
disclaimer: I know most of this is based on mistakes and whatnot, but that's sorta how you play this MU, and the best way to go about it as Lucario imo. Fox isn't going to let you use your tools in a normal toe to toe unless you space and pull off some good mindgames lol.
sideB falling is a good option, because lucario can actually get some good momentum from landing on at low percents, pretty much combos into his dash grab, dash attack, fair strings, etc. if you land it, it's risky since fox moves a lot though lol (that's where you need to use more of that ASC threat to make him guess a bit more)
ASC I think actually might have some good psychological applications in this MU, if you charge AS behind him on crossup, fox has a tricky guessing game of whether to shine, jump away, or continue shielding (or punish if he calls the bluff), and with that you can shield cancel -> SH aerial several responses since you can shield cancel it immediately, but that's sorta a player based thing and not really a MU thing
Fox's advantage for sure, I like taking fox to lylat personally (alleviates a little on laser camp because of the tilting, and it messes around with some of his recovery options, while the curving of our ES doesn't hurt us as much as most recoveries on the stage), I sorta like Yoshi's too just because of the plat allowing for guessing games. Avoid Halberd and imo delfino is dumb too, unless you plan on using MK maybe.