The dynamic evolution of the lamellar eutectic of binary alloys in directional solidification is studied in detail using the Monte Carlo technique. The simulated results can be summarized into two aspects: (1) the lamellar spacing λ is found to be inversely proportional to the chemical potential difference △μ, predicting a linear relationship between the kinetic supercooling △Tk and total supercooling at the solid/liquid (S/L) interface; (2) as the solidifying velocity R is low, the dynamic product λ2R shows a considerable dependence on temperature gradient GT in the liquid in front of the S/L interface, although this dependence becomes much weaker at a high R.