The problem of observer design for Lipschitz nonlinear systems is considered. A new dynamic framework which is a generalization of previously used Lipschitz observers is introduced and the generalized sufficient condition that ensures asymptotic convergence of the state estimates is presented. The equivalence between this condition and an H-infinity optimal control problem which satisfies the standard regularity assumptions in H-infinity optimization theory is shown and a parameterization of all possible observers is also presented. A design procedure which is less restrictive than the existing design approaches is proposed, and a simulation example is given to illustrate the observer design.