  In this article, we consider a generalized First-passage percolation model,
where each edge in $\mathbb{Z}^d$ is independently assigned an infinite weight
with probability $1-p$, and a random finite weight otherwise. The existence and
positivity of the time constant have been established in [CT16]. Recently,
using sophisticated multi-scale renormalizations, Cerf and Dembin [CD22] proved
that the time constant of chemical distance in super-critical percolation is
Lipschitz continuous. In this work, we propose a different approach leveraging
lattice animal theory and a simple one-step renormalization with the aid of
Russo's formula, to show the Lipschitz continuity of the time constant in
generalized First-passage percolation.
