Step by step:
1. Wet the leather. No need to soak it for any length of time. Running it under the tap for a second or two, front and back, is enough.
2. VERY IMPORTANT - let the leather dry for a while. Before you wet it it was a light tan color. Water darkened it a lot. Let it dry until it's about half-way back to its original color. At THAT point it will be almost as squishy as modeling clay.
3. Use a large diameter rolling pin, the heavier the better. Marble pastry pins are great for this, but even a piece of 3-4" PCV pipe will work. Now start rolling on the smooth side of the leather. Roll from end to end evenly, bearing down on the roller. Do this for 4-5 minutes, not just one minute. This will firm up the leather. If you are going to use this for a bare leather strop, roll it for 10-15 minutes. The rolling will force more silicates to migrate to the top of the leather.
4. Let it dry naturally, then glue to a backing or use as a hanging strop.
Keep in mind that any natural oil... ANY oil... is going to soften the leather. Makes no difference if it's Lexol or Olive oil. Lexol is more compatible with leather. Olive oil won't hurt it. But both will soften the leather... Soooo... if you really want a good firm strop, but need to put some sort of strop conditioner on it, dab it on a finger tip and rub it out well. Don't paint it on with a brush, or rub it on with a saturated cloth, or pour it on and rub away the excess. None of the above will harm the leather, but they will significantly soften the leather more than is needed to preserve it. The strop conditioner I use on my grandfathers old hanging strop has the consistency of thicker Vaseline, and I use less than a pea-size for the entire strop once a year. My grandfather used it every day as did my dad. I'm guessing that this stop is about 75 years old... and the leather looks brand new.