Yes, just check the ingredients.It's usually labeled as 'Poultry Dust' and always available at TSC in this area anyway.
You don't need to treat the coop for lice, they pretty much stay on the birds.
I doubt the lice alone killed the bantam, they don't feed on blood like mites-they feed mostly on skin and dander, could be a plethora of reasons a bird succumbs during a cold spell.