In this paper, we investigated the adaptive exponential synchronization problem of impulsive coupled neutral stochastic neural networks with Lévy noise and probabilistic delays under non-Lipschitz conditions. A stochastic variable with a Bernoulli distribution was utilized to transform the information regarding probabilistic delays into a model featuring deterministic time delays and stochastic parameters. In the context of adaptive controllers, exponential synchronization conditions depending on the delay, noise intensity, and impulse factor were derived using Lyapunov-Krasovskii functions, the nature of Lévy noise, and some inequality methods. To provide further support for the proposed approach, two numerical illustrations were presented.