Ken, my lye baths are outside, placed inside my 5 foot perimeter fencing, with clearly posted No Trespassing signs on the fence. :)
They are placed in a protected no traffic area, snapping lids on at all times, with bungee cords attached over the lids to keep them securely in place.
Many folks leave them outside in the coldest of temperatures.
I prefer to empty mine for the winter, but I haven't got to it yet this year.
Next few days, hopefully. I err on the side of caution, and don't want to risk hard freezing cracking the plastic of the Rubbermaids.
If I were using a heavy plastic 30 gallon drum, I probably would leave it in place.
When I set up my heated LB in the garage, I have it on a furniture dolly so I can move it if needed. The Lye Bath will work more effectively at warmer temperatures.