In my opinion you could have it as a restricted protein, as long as you check the package and make sure there aren't any additives in it. Smoking is just a preparation method so I can't see why you couldn't have it.
You got me all excited there when you mentioned lox. One of my favorite meals (and one that I miss very much) is lox, bagels and cream cheese. When we were home for Hanukkah this year my mom was making this wonderful brunch which included lots of lox. I read the package that it came in and sugar was listed on the package. I was extremely disappointed, so if it's packaged lox I would read the label before eating.
Well, after all that discussion, I ended up not eating it. Thought I really wanted it. Has a minuscule taste, and changed my mind. Maybe on a bagel with the works when we get to goal on our "free days". That's how I like them too Dana!