If I conquer with Irelia as my Legend while it's ready, can I put the "When I conquer, pay 1 to ready me" effect on chain, use Discipline on my unit, use Irelia Legend to ready it by paying one power?

Yes — the whole sequence works.

Conquering puts the Legend's "When you conquer, you may pay [1] to ready me" trigger on the chain (Rule 383.4.c.2.b), and you choose at finalization whether to perform it. Since the Legend is already ready, that ready does nothing by itself (Rule 415.1.c) — but if you pay [1] and leave the trigger on the chain, it resolves after Blade Dancer exhausts the Legend (LIFO), so the Legend ends the chain ready again.

While that trigger is pending the state is closed, but Discipline has [Reaction], so you can play it and choose your unit. That choice triggers Blade Dancer ("When you choose a friendly unit, you may exhaust me and pay [A] to ready it"), letting you pay 1 Power and exhaust the Legend to ready that unit. One catch: the unit must actually be exhausted — readying an already-ready unit does nothing (Rule 415.1.c). And note the conquer trigger readies the Legend itself; the "ready your unit" part comes from the Blade Dancer trigger that Discipline's target choice creates.