Tawn was a brand manufactured by McKesson & Robbins. They produced a line of grooming products for men; cologne, shampoo, hair dressing, talc, etc. Accurate production dates seem to be elusive, but I do know the company was doing business in the early 1930s, and the Tawn product line was launched in 1947.
The plastic tub might be Bakelite, I did not test it. The lid screws on with a ½ turn and snugs down securely. The soap is undoubtedly a tallow-base creation and my own experience is that this is old-school top-tier product that holds its own in any arena.