CAN ANYBODY TELL ME IF THERE IS ANY DANGER IN BREATHING IN THE FUMES BEING FROM THE LYE SOLUTION?
I would expect it is not a good idea to take a big whiff of the stuff - but I don't even smell anything when I am dipping my pretzels. Keep in mind, the solution is about 3 TBS lye to 1 liter of water. It is a very, very weak solution. Typical drain cleaners are 20-40% lye in solution. This is part of the misunderstanding people have. Lye is safely used in food production.
Lye is sodium hydroxide, it is not volatile at all, and there are no fumes formed when it is dissolved in water. That being said, bottle of sodium hydroxide, although it is typically sold in pellet form, may contain microparticle which could be lifted by the regular airflow and inhaled - that woud be unpleasant, although I don't think it is probable. Besides, lye slowly react with carbon dioxide in air forming sodium bicarbonate - baking soda, and it will happed to smaller particles much faster (hence pellets). So, basically, fear not, it is perfectly safe to breathe when you're using it.