Let $\mathscr{H}$ be an infinite-dimensional complex Hilbert space and $𝔄$ be a standard operator algebra on $\mathscr{H}$ which is closed under the adjoint operation. It is shown that every nonlinear $*$-Lie higher derivation $𝒟={\left\{{\delta }_n\right\}}_{n\in \mathbb{N}}$ of $𝔄$ is automatically an additive higher derivation on $𝔄$. Moreover, $𝒟={\left\{{\delta }_n\right\}}_{n\in \mathbb{N}}$ is an inner $*$-higher derivation.