  In this article, we prove a lower bound for the fluctuations of symmetric
random walks on dynamic random environments in dimension $1 + 1$ in the
perturbative regime where the walker is weakly influenced by the environment.
We suppose that the random environment is invariant with respect to
translations and reflections, satisfies the FKG inequality and a mild mixing
condition. The techniques employed are inspired by percolation theory,
including a Russo-Seymour-Welsh (RSW) inequality. To exemplify the generality
of our results, we provide two families of fields that satisfy our hypotheses:
a class of Gaussian fields and Confetti percolation models.
