  We introduce a method for translating any upper bound on the percolation
threshold of a lattice $G$ into a lower bound on the exponential growth rate
$a(G)$ of lattice animals and vice-versa. We exploit this in both directions.
We improve on the best known asymptotic lower and upper bounds on
$a(\mathbb{Z}^d)$ as $d\to \infty$. We use percolation as a tool to obtain the
latter, and conversely we use the former to obtain lower bounds on
$p_c(\mathbb{Z}^d)$. We obtain the rigorous lower bound
$\dot{p}_c(\mathbb{Z}^3)>0.2522$ for 3-dimensional site percolation.
