This paper proposes a multilane traffic flow model based on the notions of conservation laws in Lagrangian coordinates. Both the mathematical formulation and the graphical representation are provided. A logit choice model is applied to describe drivers' lane choice probability. The lane changing rate is estimated by employing the Incremental Transfer (IT) principle and the lane choice probability model. The numerical implementation of the model in the case of two lanes is discussed. The simulation results reveal that the proposed Lagrangian model is able to describe lane changing dynamics of vehicle platoons; while the lane changing equilibrium curve at the macroscopic level is consistent with that from the multilane Eulerian model as well as the observed data on the highway.