Leg stiffness will be changed with walking speed but it increase with speed (positive relationship) or may be decreased with speed (negative relationship).
I do not understand what the "leg stiffness". When it comes to muscle rigidity, it obviously varies depending on the phase of step with the activity of nerve impulses. And for the different muscles that activity is different in different stages of step. Write You about "mean" stiffness?
Gait analyses studies shows that leg spam or increase in muscle tone decrease stride length, stride width and increase double support time that will decrease walking speed.
I dont know if you mean that. but there is several studies explain this relationship. https://www.google.com.eg/search?safe=off&q=leg+stiffness+and+walking+speed&spell=1&sa=X&ved=0ahUKEwjtzu2RmsHRAhWBDMAKHQwaBLkQvwUIFSgA