If you want to approximate the past, you could get some leather welding gloves, cut through the seams, and fold them up, to make a pad. The more you fold the leather, the thicker the pad becomes.
Also, it looks like you may be striking on top of your leg. There is a photo of Ishi, somewhere, that shows him sitting on the ground, with knees bent over to the left. He is propping a stone or nodule on the right side of his thigh, while holding a hammerstone. Most people probably do not have the hip flexibility to carry out this practice. It takes some getting used to.
Also, there are other illustrations which show natives sitting on the ground with the left knee, and leg, propped upright. The left hand holds the biface, and rests against the inside of the left leg. The upright left knee acts as a brace against the blow. If you are using a percussor, such as a hammerstone, this would be considered a form of "freehand percussion with rest".
Also, if you need more force in the blow, you can always hold the edge of the stone against a block of wood, held between the legs, or resting on the lap. The method is reminiscent of bi-polar percussion, though you might not produce true pole to pole flakes. Early pioneers saw Indians work glass by holding the edge against a boulder, and then striking the opposite edge with a pebble. Indians in California worked obsidian by the same method, while holding the edges of the stone against a slate anvil. In archaeological studies, one can still see anvil stones, in those obsidian bearing areas, with pitting on the sides, where the obsidian edges had been positioned.
Also, if you have to strike really hard, you may do better with hammerstone processes. If you use a block anvil on your lap, you can rest the edge of the stone on top of the anvil, while swinging away from the upper edge. Or, you can hold an edge against the side of the block anvil, while swinging the hammerstone downwards, and striking the edge.
Each process has its advantages, and disadvantages, depending on what you are trying to do. If you are using a lap anvil, padding may not be necessary. But, you should still drape something over your legs, to keep the fragments of sharp debitage from sticking to your skin.
