Robert, a number of our members keep their lye tanks inside. (kitchen or basement) .
I always mix mine outside, because when you initially mix lye with water, the exothermic reaction gives off fumes. After mixing is complete, I have not experienced any noticeable fumes or smell. Last winter I had a 5 gallon bucket of lye sitting in my kitchen, with lid, with no problems. Will probably have a small one again, in the next few weeks, in the kitchen.
My larger capacity lye baths are outside, or in the garage (e.g. the current heated lye bath).
Now that is not to say that lye is totally harmless to humans. The solution is very caustic (high PH = Base), and can cause burns to the skin and human tissue, which is why I wear a full face shield to protect my eyes and face, and chemical gloves to protect my hands and forearms. I also keep a source of running water close at hand, and a spray bottle of 100% vinegar (acetic acid) within reach in case of accidental splash onto skin.
Acid is at the other end of the spectrum with low PH... and is just as nasty at low PH.
Operating an Electrolysis will produce Hydrogen as a byproduct, and should not be placed or operated in a confined space. Operation should be in a ventilated area, so that the hydrogen is dispersed and cannot build up (as in a confined area). Hydrogen can and will go boom! Nor should an electrolysis be operated near an open flame source without proper ventilation. I have run my electro in the garage, with the kerosene heater burning, and have not had any issues... but then my garage is extremely self-ventilating... (meaning, poorly insulated with lots of airflow from the outside) ;D I always turn off my battery charger before touching or removing any connectors, to avoid random sparks that could ignite any residual hydrogen.
The bottom line is, that you should only do what you feel comfortable with regarding lye and/or electrolysis.
