My understanding is that lye and baking soda are used in water baths when making bagels and pretzels in order to reduce PH. I got some lye and it is working wonders but it is a bit of a hassle to use it safely, which is non-negotiable. I know lye is far more alkaline than baking soda, but could I simply use a much greater amount of baking soda? Is PH the only variable here?
Yes, the pH is pretty much the only variable - especially in the pairing you are describing, since both are sodium salts. I suspect you may get taste effects if you were to use, say, a potassium-based salt, but that's not relevant here.
Since pH is the variable we need, they are not interchangeable. You need a strong base to get a good crust on a pretzel, and if you only use baking soda, with its low pH, you will end up with a crust that is between a pretzel and a simple boiled bagel. Of course, if this result is good enough for you, then you can do it this way and enjoy your food. But if you want the authentic, dark brown, chewy, glossy crust, you have to go with lye.
Update For a bit more background: Not every base is created equal. There are many salts which, when dissolved, create a solution that is only weakly basic. They have the chemical property of a "final" pH which is independent of concentration - once you reach it, it doesn't matter if you keep adding more and more of the salt to the water, it stays at the same pH. The exact value of the final pH of a base is determined by the ions into which it separates when dissolved. The basic and acidic ions of the salt both have an intrinsic chemical property called dissociation constant.
To cite bob1's comment,
For H2CO3 [baking soda] these are H2CO3 <-> HCO3(-) + H(+) and HCO3(-) <-> CO3(2-) + H(+) with dissociation constants of of 6.37 and 10.25 respectively. pH = 1/2(pKa + pKb).
This means that baking soda creates a solution with a pH of 8.31, which isn't very much. Even if you keep adding more baking soda, the pH won't get higher. So there is no way to use baking soda to get even close to the effect of a 4% lye solution, which has a pH above 13 - that's a huge difference.
Here is a way to make use of baking soda when you need an alkaline, such as for pretzels. McGee includes some explanation of the chemistry. Baking your baking soda first, gets you a pretty close, flavor and color-wise, if you are making pretzels. It's a good hack for ramen too. Just spread a layer of baking soda on a sheet pan, and bake at 250F - 300F for an hour. Cool and use.