We establish new lower bounds for the normal approximation in the Wasserstein
distance of random variables that are functionals of a Poisson measure. Our
results generalize previous findings by Nourdin and Peccati (2012, 2015) and
Bierm\'e, Bonami, Nourdin and Peccati (2013), involving random variables living
on a Gaussian space. Applications are given to optimal Berry-Esseen bounds for
edge counting in random geometric graphs
