Observer synthesis for nonlinear Lipschitz systems with time-varying sampling is studied. To establish the exponential convergence of the observer, in this paper, we model the impact of the sampling uncertainty by a reset integrator. First, generic conditions for stability of a sampled data system are recalled. Second it is shown how to derive tractable numerical conditions to analyze the robustness of a continuous-time Luenberger observer when the sampling is discrete and time-varying. Then it is demonstrated that this emulation approach can be passed over allowing for the direct computation of an observer gain. Simulations and comparisons with related articles show the efficiency of the proposed methodology.