This note proposes a cascade observer for a class of nonlinear systems with global Lipschitz nonlinearities in the presence of delayed output measurements. The head of the cascade is a high gain observer while the remaining systems are state predictors providing an estimate of the actual state. The key feature of the proposed observer is the introduction of a matrix design parameter that allows to tune the prediction process dominant dynamics with an identical simple structure for all the predictors. The design of the observer is carried out by considering a set of conditions under which the exponential convergence to zero of the observation error is established. In particular, it is shown that the number of the subsystems in the cascade observer depends on the size of the delay and the Lipschitz constant. The observer is first designed assuming a constant time delay. The underlying design approach is then appropriately adapted to deal with the time-varying delay. The effectiveness of the proposed observer with respect to two existing cascade observers is particularly highlighted through a comprehensive comparative analysis and simulation results.