I've been making my own soap for going on two years, using a no-cook recipe based on Lye (RD), Olive Oil, water, and whatever one wants to use for fragrance and other healthy purposes; I've been using chunks of my own grown Aloe and some Essential oils like Lavander, Sandalwood, etc.
I've not yet ventured into using Lard, I'm assuming a lard-made soap requires cooking, but I may be wrong. As for using a stick-blender, try to buy a good quality one. My mother received one as a present but never used it and gave it to me. The poor thing smoked after about 2 minutes of blending my soap recipe. I've had good success using a regular juice blender, but this requires doing several "loads" since I make a large batch (over 140 ounces of liquids total per batch), I've also used a regular hand-held mixing blender with success, but, it does not blend as fast as a juice blender or stick blender, so it still takes almost an hour of blending with it to get to traces AKA "ribbons".
Here is another site that focuses on home-made soaps, shampoos, etc. It includes a handy "lye calculator" that helps one adapt the quantity of ingredients to their preference.