This letter deals with observer-based control design for a class of Lipschitz nonlinear systems with nonlinear outputs. Based on the use of Lipschitz property and Young inequality in convenient ways, a novel LMI-based design technique is proposed. The method is also mainly based on exploiting new matrix-multiplier techniques, which allow the involvement of extra decision variables in the LMI conditions while improving the feasibility of the proposed LMI conditions. All these mathematical tools, used in a judicious manner, made it possible to obtain less conservative LMI conditions compared to previous LMIs existing in the literature. Furthermore, the established approach ensures a real-time ISS bound on the observer-based stabilization error. The validity and superiority of the developed methodology are validated through a numerical example.