For the reaction,  
$$\ce{M -> M+ + e-}$$  

the heat liberated is highest for lithium owing to its high negative $E^\circ$ value so one would think that the reaction must be most vigorous.   

The reason behind the more violent reactivity of potassium rather than lithium lies in _kinetics_ and not in thermodynamics. 

No doubt, maximum energy is evolved with lithium but the vaporization and ionization will also consume maximum energy (the melting point and ionization energy of lithium are the highest) and so the reaction proceeds gently. On the other hand, potassium has a lower melting point and the ionization enthalpy. The heat of reaction is sufficient to make them melt. The molten metal spreads over the water and exposes a larger surface to water. Also, the hydrated radius of lithium is the greatest out of all alkali metals. This reduces the ionic mobility which in turn reduces the speed of the molten metal.  
  
That's why potassium gives a more violent reaction with water.
***  
Reference:
  
- Kumar, Prabhat _Conceptual Inorganic Chemistry_; Shri Balaji Publications: Muzaffarnagar, U.P., 2014.