The molecular field theory of the Frederiks transition has been developed based on the Lebwohl-Lasher nematogen model and localized mean field approximation. We found that it needs five order parameters to generally describe the nematic system with boundaries. For the splay type of cell configuration, two of these order parameters are zeros. The theoretically calculated results are further confirmed by corresponding Monte Carlo simulation using Lebwohl-Lasher nematogen model as the prototype of the liquid crystal and the agreement is quite good considering the simplicity of the theory. The experimental law and the predictions of classical anisotropic continuum media theory are also reproduced by the present molecular field theory. Therefore, the results obtained in this paper lend a support to the general validity of the Lebwohl-Lasher nematogen model for the theoretical studies of small molecular liquid crystals.