  In this paper, we address rare-event simulation for heavy-tailed L\'evy
processes with infinite activities. The presence of infinite activities poses a
critical challenge, making it impractical to simulate or store the precise
sample path of the L\'evy process. We present a rare-event simulation algorithm
that incorporates an importance sampling strategy based on heavy-tailed large
deviations, the stick-breaking approximation for the extrema of L\'evy
processes, the Asmussen-Rosi\'nski approximation, and the randomized debiasing
technique. By establishing a novel characterization for the Lipschitz
continuity of the law of L\'evy processes, we show that the proposed algorithm
is unbiased and strongly efficient under mild conditions, and hence applicable
to a broad class of L\'evy processes. In numerical experiments, our algorithm
demonstrates significant improvements in efficiency compared to the crude
Monte-Carlo approach.
