Instead of using fence staples you might want to use screws and washers. We did that and used a ton of washers. I read somewhere that raccoons and probably other predators can rip those staples out pretty easily but not with screws and washers.
Hint: at Home Depot, you can buy whole boxes of washers. If you reach in behind the loose ones they have unopened boxes and it's a LOT cheaper than buying the washers by the "each".
X2 !
Or... Stapel hardware cloth on and then overlap with lath and screw in.