We consider the event-triggered state and disturbance simultaneous estimation problem for Lipschitz nonlinear systems with an unknown time-varying delay in the state vector. For the first time, state and disturbance can be robustly estimated by using an event-triggered state observer. Our method uses only information of the output vector when an event-triggered condition is satisfied. This contrasts with previous methods of simultaneous state and disturbance estimation based on augmented state observers where the information of the output vector was assumed to be always continuously available. This salient feature, thus, lessens the stress on communication resources while can still maintain an acceptable estimation performance. First, to solve the new problem of event-triggered state and disturbance estimation, and to tackle unknown time-varying delays, we propose a novel event-triggered state observer and establish a sufficient condition for its existence. Then to overcome some technical difficulties in synthesizing observer parameters, we introduce some algebraic transformations and use inequalities, such as the Cauchy matrix inequality and the Schur complement lemma to establish a convex optimization problem in which observer parameters and optimal disturbance attenuation levels can be systematically derived. Finally, we demonstrate the applicability of the method by using two numerical examples.