Lye is also used to make bagels (not all bagels, but definitely it’s a thing)
Lye may have been the original finishing agent. Much more commonly used for various cooking and other purposes in the past.
While we have some great bagels here in the US there are plenty that are not real ‘water bagels’ as we knew them back when I was young. Major cities have more bagel makers that make them the traditional way but plenty are made as single rising rolls from mixes. They can occasionally be almost as good but tend to be more bread-like.
Over the years I’ve seen the size of bagels increase, same as donuts and other bread forms.
And granny from the Beverly Hillbillies would use Lye to make soap out by the “seement pond” and her cauldron.
I’ve only used baking soda at attempts to make bagels and pretzels. A lot of disappointment when the folds of the pretzels detach upon extraction. Just as with Bagels in the UK, one can find facsimiles of (soft & salty) pretzels here. But nothing like the kind the long-gone pretzel vendors outside Central Park immortalized on Steely Dan’s “Pretzel Logic” cover.
Update 