Which Rod am I using?
I have noticed that when you cast with one rod, then switch it out to another rod, the lure stays out.
Then I switch it out, just by replacing it in the inventory slot:
Which rod am I using when I switch rods? Am I using the first rod(unenchanted) or the second(enchanted)?
Visually the same bobber seems to stay out from the first cast, but the durability damage is only taken on the rod that you reel in with.
For the sake of balance I'd imagine that it would be the second rod, being the one that takes the damage, that determines your luck. This would also be consistent with how other enchants on other tools work, in that it's the sword your holding when the mob dies, or the pickaxe you finish mining the block with (before they out patched switching tools mid-mining). I'm also pretty sure that the bobber entity stores no data about the enchants of the rod it was cast with.
To be sure, I did some testing. First with a normal unenchanted rod, then a rod enchanted with Luck of the Sea III, and then switching from the unenchanted to the enchanted one. This table shows the results:
So it seems that the enchantment applied is the one you reel in with, rather than the one you cast out with, supporting my initial theory. I may add more data to the table in the future when I do more fishing.