In this paper, a new type of continuously variable valve lift (VVL) system is presented. The mechanism comprises a standard roller finger follower, the camshaft, and an intermediate rocker arm used between them. When the adjustment shaft rotates, the intermediate rocker arm is repositioned with respect to the cam and the roller of the rocker finger. This means that, when the rotation angle of the adjustment shaft is controlled, the valve lift height is also controlled. The intermediate rocker arm is equipped with a special developed contact surface, which is one of the novelties of this paper. The profile of the contact surface is analytically determined using the theory of the envelope curves. Using a certain cam profile, the kinematic analysis of the mechanism proceeds, resulting in the family of the valve lift laws. This paper also establishes the general conditions to design a variable valve timing (VVT) mechanism with continuous VVL and mechanical actuation. Numerical simulation shows that the mechanism continuously varies valve lift height and timing phases, while the valve's opening time remains constant. The last parts of the paper are dedicated to different aspects concerning the elastohydrodynamic lubrication and valve train dynamics. The study is performed by comparing the optimized cam and a standard harmonic one which achieves the same maximum displacement of the valve. The optimized cam ensures better safety in functioning, a smaller preload, leading to a greater oil film thickness, and not causing excessive deformations in the engine. The calculation model is a general one, and it may be applied to other mechanisms with similar configuration.