Are jackets required for men at Herbsaint, Palace Cafe and Lilette for dinner???
While you might wish to check with each, I do not anticipate that they would be. However, they might be fitting with other male diners - something totally different, than "required."
Nobody cares anymore..some painter's pants, oil-splashed espadrilles, tasteful "message shirt" from Bourbon Street, fanny pack held together with duct tape..
Palace is the only one I'd not dress up for but I'd proably be wearing a coat and tie anyway.
You're fine without, though service does ratchet up a notch, sometimes, when you're well dressed (and maybe Hazelhurst won't sob so bitterly...). You certainly won't be out of place wearing one, even in the bars and clubs afterwards. Dressed up and slumming it is always acceptable.
On a strictly practical note, NOLA isn't exactly hot this time of year. I'm often more comfortable wearing a jacket just because places can be chilly.