Uhm...I would not. You can go to your local thrift stores to see if they have any old stainless steel pots or bowls. Bring a magnet with you to be sure it is real steel and not aluminum. Look around for old crock pots and stick blenders while you are there. If you can't find stainless there, I noticed Walmart had a 4 piece stainless steel bowl/colander set online for $19 or $20 yesterday. You could grab a set of those, or go to Walmart and get a cheap stainless steel pot for $7-$10.
The lye/soap won't "ruin" the pot that I know of, but I would err on the side of caution and use a separate pot just for soap. Besides, you don't need anything causing friction between you and your mom.
Do read The Efficacious Gentleman's article about equipment, it is a good one. Thorough yet easy to read without overwhelming you with information.
Also go to the dollar stores in your area. Look for plastic mixing cups with a 5 in the little triangle on the bottom, plastic spoons, gloves, safety glasses(NOT optional), and silicone spatulas. You are going to want to get some sort of container to hold all your soaping equipment unless you can dedicate a cabinet or closet to the endeavor. Buy one large enough to hold everything with a bit of room left over for all the goodies you are going to find absolutely necessary.
Get yourself a good digital scale. This is the one item I am going to tell you to buy the most expensive one you can afford. You must have one that can change from ounces to grams if you are in the US, but if elsewhere, just grams is sufficient. Having one with no auto turn off is optional, but would be wonderful.(Wish I had known such existed when I bought mine!)
You are probably thinking that you are going to just try this this one time, so none of this is necessary, right? I would be remiss if I did not warn you now that soapmaking is addictive. And, since you are already on this forum, you are probably already addicted. So, you may as well go ahead and get some dedicated equipment.