Charles,
What kind of problems are you concerned about? Will it evaporate and cause your pipes to corrode? No. Will a leak cause a problem? Yes, maybe a big problem. Is it toxic? Well, it could kill you if you drink it. What if the nephew gets into it? That would be a problem.
My lye bath is in the cellar year round. I use a 35 gallon HDPE drum, so the probability of a leak is fairly low. If you use a cheap storage tub with thin walls, you may want to consider secondary containment in case the container splits or a leak develops.
I do not worry about evaporation, so I never cover my drum. I probably should because every now and then I leave the cellar door open and a neighborhood cat sneaks in. Remember, the sodium hydroxide (lye) is a salt and it does not leave the bath as the water evaporates. However, it is consumed in the reaction that converts grease to soap (ref The Casting Call Vol 5 No 2).
Jeff