This paper investigates the distributed secure filtering problem for discrete-time nonlinear systems over wireless sensor networks subject to deception attacks and switching topologies. The investigation considers stochastic attacks in two network channels, that is, on measurements from the plant to sensors and on state estimates among the sensor nodes. Moreover, the network topology for the estimates sharing is assumed to be time-varying, based on a homogeneous Markov chain. An event-triggered distributed set-membership filtering structure is formulated that ensures the estimation error to remain in a bounded ellipsoidal region in the presence of two-channel attacks, switching topologies, and unknown but bounded perturbations. The conditions for boundedness of estimation error are derived for a class of nonlinear systems satisfying the Lipschitz condition globally. The obtained results are also extended to nonlinear systems that satisfy the Lipschitz condition locally in an ellipsoidal region. The filter design conditions are then converted into a convex optimization problem to find desired filter gains as well as optimal estimation ellipsoids. To the best of our knowledge, the secure ellipsoidal set-membership filtering technique is being investigated for the first time for locally (ellipsoidally) Lipschitz nonlinear systems over WSNs subjected to two-channel stochastic deception attacks. Finally, a simulation example is provided to verify the results.