Frequent changes in process dynamics make re-identification of a dynamic model prerequisite for sustainable application of model predictive control. When the process needs to comply with a particular operating range for product specification or safety requirement, the model should be re-identified in closed-loop. In addition to potentially poor exciting signal for the identification, another challenge is that many industrial processes are multi-rate systems whose variables have different sampling intervals. This paper proposes a re-identification method for dual-rate non-uniformly sampled systems under closed-loop with a MPC controller by lifting the original system. The proposed identification method provides accurate and realistic model compared to the model used before the identification is conducted. We also compare the identified model and the existing model by applying to MPC.