  In this paper, we investigate the generalized covariant entropy bound in the
theory where the Einstein gravity is perturbed by the higher-order Lovelock
terms. After replacing the Bekenstein-Hawking entropy with the Jacobson-Myers
entropy and introducing two reasonable physical assumptions, we showed that the
corresponding generalized covariant entropy bound is satisfied under a
higher-order approximation of the perturbation from the higher-order Lovelock
terms. Our result implies that the Jacobson-Myers entropy strictly obeys the
entropy bound under the perturbation level, and the generalized second law of
Lanczos-Lovelock gravity is also satisfied when the Einstein gravity is
perturbed by the higher-order Lovelock terms.
