Lure/Luck of the Sea enchantments cannot be applied

I'm trying to enchant a fishing rod, but the Enchanting Table (no bookshelves are nearby) won't let me apply anything but Unbreaking. I have enough Lapis and XP, and the option lights up in the UI, but hovering over the option doesn't present the enchantment name, and clicking it has no effect. The attached screenshot demonstrates this.