If you are using an existing recipe, as described in the question, and want to make a smaller batch, just keep the same proportions; if you start with say half the oil, use half the lye (and any other ingredients), and don't make any substitutions (like a different kind or mix of oil).
However, I would recommend not using used oil, at least for your first attempts at soap making. There are several reasons:
Used oil will be adulterated with substances from whatever foods were cooked in it. You can filter out bits of stuff and boil off any water, but various compounds from the foods will remain in the oil. When you react the oil to make soap, those compounds can affect at least the smell and color (not in a good way), and sometimes other characteristics if there's more than trace amounts.
In an earlier answer, I distinguished between "primitive" and "modern" soap. Primitive soap can be made from any fatty material you have laying around, including used oil. But any impurities in it can make for nasty results. It will still act like soap. The odor and color will generally wash off whatever you're cleaning if you rinse it well. So at least the washed item won't smell worse than it did before you washed it, especially if you hang it in sunlight for a while or douse it with some perfume. That was adequate when this was the only soap you had. You can still make crude soap this way as a novelty or to explore life of yesteryear, but be prepared for surprises and to throw away the worst results.
While you're learning the art of soap making, predictability is important to learning, and success is important to motivation. If you start with pure, known ingredients and use precision, you can replicate satisfying results and have a basis for tweaking them the next time. Primitive soap will turn out a little different each time, even if you measure the ingredients carefully. Results will be very hit or miss, and you won't learn from the process.
People sometimes worry about wasting ingredients on their first few failures. Starting with waste ingredients is a way to see how the process works and decide if they're interested in pursuing it. That's likely to lead to the first attempts being failures and deciding that it isn't worth pursuing. If you start with making modern soap, you will gain some experience making good soap in a controlled way, which will give you a basis for comparison. Then experiment with primitive soap and you'll be able to recognize what is a deviation from the expected results.