If you're implying you got hit before your zair hit: Execution matters, you can connect with everything I mentioned before your invinicibility ends. Abusing your invincibility is especially important against characters with disjointed hitboxes, because it allows you to go right through their swords and start doing Lucas stuff, if they rely on their range advantage to keep you from the stage. Also, you don't have to jump up high to use the ropesnake.
Crouch canceling could be a problem because we can't ledgedash->grab properly, but magnet and dair can deal with it if you can reach them and ledgejump->DJ->magnet adds quite a bit of reach to your magnet compared to just ledgejumping before it.
I also figured I should expand on what I said, because not everything is obvious and there's a ton of stuff to be said about every single option you have (and I like writing stuff):
- Ledgehop/-jump aerials: In either case, you'll usually want to DJC your aerials unless you're trying to go above the opponent (which is very situational). You'll land sooner and are invincible anyway, so you can't be hit out of your DJ. A wrong timing for a ledgehop DJC leads to a suicide, but it's pretty easy to hit the right timing (unless you go for the really low one obviously). For ledgehop fairs the hitbox doesn't even come out later than had you not canceled your jump as with any timing where your hitbox comes out above the stage you'll also land on the stage. I mostly prefer fair for the range especially against swords, but if your opponent is ccing you'll probably want to use dair instead. Dair though is more dependent on your opponent's position and is harder to hit with during invincibility. Ledgehop (ledgedrop->DJ) aerials don't hit as far into the stage as ledgejump(->DJ) aerials and land later, but come out faster. The difference between perfect execution and however little imperfect execution (for landing soon) is also larger with ledgehops. Different timings give you different flight paths. I'd guess that most of the time you want to do ledgejump->DJC fairs and ledgehop->DJC or ledgejump->no DJC dairs, but the ideal choice depends on the positioning etc. of the opponent.
If you miss a fair with a fast landing timing and good execution you'll still have a bit of incvincibility left after the landing lag (comparable to that of Lucas' ledgedash).
- Ledgehop/-jump magnet: About as fast as ledgejump-aerials, but has less range than fair. On the other hand, it's magnet so massive advantage on shield, hits might lead to gimps, it's not really cc-able and with perfect execution you can still do a DJC fair during your invincibility. You end in the air after it instead of on the ground due to the JC, which might be better or worse. Also, depending on the timing you can either end with an aerial magnet (into DJ) or grounded magnet (into jump). Ledgehop and ledgejump are about equally fast (ledgehop one frame faster) and ledgejump->magnet has a bit more range. Situation and preference will be deciding what to use I guess.
- Airdodge->Zair: This option has a huge reach, but dodge to far in before zairing you're vulnerable before the hitbox comes out. Again you have quite a few options how to use this one. You can either ledgedrop->airdodge diagonally up, which will hit quite soon but only cancel late (only do this if it won't be just punished on hit) or you can ledgehop/-jump before the airdodge. In the latter case ledgejumping and then airdodging horizontal to the stage gives you (near) immediate cancels, but ledgehopping is not far off and could still realistically be used if preferred. You can also just ledgehop first and try to bait an reaction before either airdodging in for a punish or tethering back to the ledge. Lots of options. Wrong executions might leave you canceling the attack before it comes out, which obviously is bad, and cc-ing is strong against the snake.
- Ledgehop->DJC PKF: I didn't try this one in practice, but it sounds okay and someone else might have more insights into it. Ledgejump doesn't work for this, because you'd either not be able to DJC it, land before the projectile comes out or take far too long. You spend more time in the air than usually and probably hit the opponent sooner than when you DJC PKF on stage, so it doesn't combo as well as it usually does, but it still is an option that doesn't look terrible.
- Ledgedash: Ledgejump->airdodge is 1 frame faster than ledgehop->airdodge and gives you 5 frames to act during invincibility, which is quite bad tbh (for comparison: Fox has 12 frames, Mario 10 iirc) and a result of Lucas strange DJ. Still - it's an option and mostly your best option if you just want to get onto the stage fast without attacking.
There actually is a technique which is akin to a very short ledgedash and gives you 10 frames of acting invincibility - much more in line with normal DJ characters. It's a double 1 frame window though, so I'm just mentioning it for completeness' sake: Ledgejump->Airdodge horizontally to the stage->Tether on frame 1 of the airdodge. I don't think it's currently worth putting the effort into it that would be necessary, but this is Lucas after all, so somebody might be crazy enough.
- Tether stall: Ledgedrop->Tether->Reel in. Renews your invincibility the fastest and is ideal for just mixing up the get up timing.
- Thunder stall: Ledgedrop->PKT->Make the Ball go into the stage (or hit yourself with it). A little gimmicky for you are not invincible the whole time, but can throw the opponent off, renews invincibility and doesn't use up tether usages, so it is an acceptable mix-up but I wouldn't use it too often.
(The frame data stuff is for 3.0 because I didn't bother installing 3.02 on Dolphin yet, but I don't think that would change anything.)