Some men go to some trouble to soften a hard soap so that it's easier to swirl onto a wet brush, thus getting enough product on the brush that a hearty lather can be made. This includes soaking rituals in which warm or hot water is applied to the puck prior to loading the brush with soap.
In my experience there are two things that can be done individually or in concert to make hard-soap lathering a breeze, a walk in the park, duck soup.
1) Prior to your shave, wet your beard as desired and then simply rub the flat of the hard soap puck directly on your unshaven whiskers. Then dip the tips of your damp shave brush into water.
(I use a re-purposed Greek-yogurt container holding about a half inch of cool water). Then face lather and as necessary again dip the brush tips into the water to add moisture so that your lather is adequately wet and not pasty. (I often dip my brush tips four or five times as I face lather.)
2) Stop rinsing your shave brush after your shave. If you keep your brush free of stubble, blood, and dead skin cells, there's no reason to rinse your brush; it won't harm the brush. Just let the existing lather dry between shaves. The dried lather is uber easy to revive by just adding water and re-whipping the lather on face or in a bowl. (I prefer to skip the bowl, which I have found to be completely unnecessary, and just more stuff that it has been a pleasure to shed.)
Using these methods can simplify and streamline your shaves -- and also save you some money if you open your mind and give value products such as Williams shave soap another try.