I think his nair can poke shields. :/
It can, but that's risky business. If your opponent angles their shield like they should, it won't poke and you'll be punished. Hell, if the shield full health, I don't think it'll poke unless your opponent doesn't expect the attack to last so long and just stops holding shield to punish too early. General rule of thumb is not to rely on your opponent not expecting something basic, though.
I would say keep hitting. If your spacing correctly, the PK fires will just keep pressuring the shield until they come out. That's when you use the zairs to set up combos and fires to push them away. Otherwise, I would try down smash in shield. It should push them back, and if they come out of shield for a punish too early, they'll get hit with the slightly more greatly ranged third hit. Not completely sure if it's a good idea, but I would just keep PK firing.
I wouldn't dsmash on shields, it's more of a ledge covering option than a shield punishing move - its even one of the worst dsmashes for punishing rolls, but exceptional at punishing spotdodge. Overall you're on the right track with PK Fire.
Lucas' PK Fire is fast, has a huge hitbox, and has two distinct hits. Opponents unprepared in the matchup won't know about that second hit, and will drop shield on the explosion thinking it's cosmetic, but like I said, "General rule of thumb is not to rely on your opponent not expecting something basic, though." Lucas is a character very much about spacing, so in an ideal situation, your opponent can shield all they want and you won't be caught with your pants down - you're not the one who is being forced to approach (at least not approach-approach). Use general mixups and mindgames if you need to put damage on or go in for that kill; reversed grabs, empty hops, dashing at them to bait the shield, etc.
Most importantly of all, never be predictable ever. If you've been dashing at your opponent's shield for a grab, or empty hopping into a grab, if they're not an idiot they're going to catch on, and you don't play against idiots, right? When you think they've caught on, dash into a nair or turn that empty hop into a zair, as far as I remember it has quite a lenient autocancel, and does decent knockback. If you're feeling really confident, turn that empty hop into a magnet, it does way more knockback and thus rewards the read better.
