Lithium has most negative electrode potential still its reaction with water is less vigorous than that of sodium
You can't just take the electrode potential as if that's going to correspond to the rate in which something is going to react. For example, why do you think that aluminum is so stable in atmospheric conditions versus iron? Aluminum forms a stable oxide layer that serves to protect it against further reaction, while iron oxide is weak, adheres poorly and is and porous. There are numerous factors which affect a rate of reaction, and they vary in different situations.
Calculating rates of reaction is a very complicated thing, and it's usually easier / more accurate to just determine the Arrhenius parameters experimentally and use those.
Reactivity with water in the sequence Li (mp=180.5C), Na (mp=98C), K (mp=63.5 C) is dictated by melting point of the metal. Electrode potential dictates the equilibrium constant between M and M+. With voltages >1 the reverse reaction can be ignored.
Here is what happens when alkali metal reacts with water from phisical perspective. It contacts water, temperature rises to 100C (boiling point of water). Lithium remains solid, whereas Na and K turn into a liquid. This liquid spreads on the surface of water creating a large area of contact. Lithium remains solid. LiOH forms on it's surface and prevents further reaction. LiOH does dissolve in water (that is why Li react with water and Al doesn't), but it takes time. At the same time both sodium and potassium leak out of the protective shell of oxides/hydroxides.