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Lake ecosystems exhibit nonlinear responses and may undergo catastrophic shifts to opposite states from which recovery is difficult. Recent theoretical and experimental developments have revealed that characterizing the resilience of ecosystems can provide a way to anticipate critical transitions. In this letter, we present a novel and practical approach that measures the resilience, i.e., the relaxation time as an indicator of a critical transition to a eutrophic lake state. Furthermore, the possible mechanisms underlying these findings are explored via stochastic resonance, namely, the signal-to-noise ratio as a function of the system parameter shows a maximum value when the noise intensity is fixed. The results show that relaxation time is an excellent indicator, and stochastic resonance occurs near a critical threshold. Our results offer a new perspective to anticipate critical transitions in ecosystems.