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

The heat liberated is highest for lithium owing to its high negative $E°$ 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** not thermodynamics. 

No doubt, maximum energy is evolved with lithium but the vaporization and and ionization will also consume maximum energy ( m.pt and I.E 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 metal. 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.
***  
**SOURCE**  
Conceptual Inorganic Chemistry; Prabhat Kumar