For multi-sensor nonlinear systems under non-Gaussian noise, a mixture maximum correntropy criterion (MCC) is proposed in this paper using the mixture Cauchy kernel function to achieve robust filtering under non-Gaussian noise. Traditionally, the MCC criterion is applied by using the prediction error of a single node as the kernel function input. However, in a distributed fusion framework, the consensus between nodes can affect the filtering accuracy due to the different non-Gaussian noise measurements at each node. To address this issue, a consensus strategy is introduced, where the error information from multiple nodes is jointly used as the kernel function input, enhancing the consensus among the nodes. Based on this criterion, the lattice Kalman filter is extended to the distributed environment. A rank-1 lattice rule is employed to approximate high-dimensional integrals in the nonlinear filter, and fixed-point iterations are used to compute the posterior estimates of the state and covariance. Finally, the proposed method is validated on the IEEE 9-bus power system model, demonstrating its superior estimation accuracy.